rtirq-20130402-1.fc19 has been submitted as an update for Fedora 19.
https://admin.fedoraproject.org/updates/rtirq-20130402-1.fc19

rtirq-20130402-1.fc18 has been submitted as an update for Fedora 18.
https://admin.fedoraproject.org/updates/rtirq-20130402-1.fc18

Package rtirq-20130402-1.fc19:
* should fix your issue,
* was pushed to the Fedora 19 testing repository,
* should be available at your local mirror within two days.
Update it with:
# su -c 'yum update --enablerepo=updates-testing rtirq-20130402-1.fc19'
as soon as you are able to.
Please go to the following url:
https://admin.fedoraproject.org/updates/FEDORA-2013-9308/rtirq-20130402-1.fc19
then log in and leave karma (feedback).

You didn't do this quite right.

1. You need to get rid of the old sysv initscript competely (or ship it in a "-sysv" subpackage, but please don't do this).  You also need to enable the sysv->systemd conversion logic:

https://fedoraproject.org/wiki/Packaging:ScriptletSnippets#Packages_migrating_to_a_systemd_unit_file_from_a_SysV_initscript

2. In Fedora 19, services should not enable themselves automatically, but instead use the new preset logic:
https://fedoraproject.org/wiki/Packaging:ScriptletSnippets#Macroized_scriptlets_.28Fedora_18.2B.29

You may or may not need FESCo approval to start your service automatically:
https://fedoraproject.org/wiki/Starting_services_by_default

If you are permitted to start your service automatically, file a bug against systemd to have it added to the distribution default preset file.

Thanks for picking this up. I have just followed upstream in this case but I will modify as you've recommended. Updates have been unpushed

Here's what I've got. We can enable by default in the audio spin kickstart - not required here

@@ -39,14 +39,11 @@ done
 
 %install
 rm -rf %{buildroot}
-install -D rtirq.sh   -m 0755 %{buildroot}%{_sysconfdir}/rc.d/init.d/rtirq
+install -D rtirq.sh   -m 0755 %{buildroot}%{_bindir}/rtirq
 install -D rtirq.conf -m 0644 %{buildroot}%{_sysconfdir}/sysconfig/rtirq
 
 # fix order of interrupts, tac was reversing the priority of the soundcards
-perl -p -i -e "s/\| tac//g" %{buildroot}%{_sysconfdir}/rc.d/init.d/rtirq
-
-# start rtirq after the alsasound startup script (starts at 87)
-perl -p -i -e "s|35 81 19|35 88 19|g" %{buildroot}%{_sysconfdir}/rc.d/init.d/rtirq
+perl -p -i -e "s/\| tac//g" %{buildroot}%{_bindir}/rtirq
 
 # high priority is 70 instead of 90 (in Fedora 17+)
 perl -p -i -e "s|RTIRQ_PRIO_HIGH=90|RTIRQ_PRIO_HIGH=70|g" %{buildroot}%{_sysconfdir}/sysconfig/rtirq
@@ -58,6 +55,8 @@ perl -p -i -e "s|RTIRQ_PRIO_DECR=5|RTIRQ
 perl -p -i -e "s|rtc snd usb i8042|rtc snd i8042|g" %{buildroot}%{_sysconfdir}/sysconfig/rtirq
 # adjust priority for udev changes, same as highest priority
 perl -p -i -e "s|RTIRQ_PRIO_UDEV=85|RTIRQ_PRIO_UDEV=70|g" %{buildroot}%{_sysconfdir}/sysconfig/rtirq
+# moved out of init.d/
+perl -p -i -e "s|/etc/init.d/|%{_bindir}/|g" rtirq.service
 
 # install udev and power files
 install -D %{SOURCE2} -m 0644 %{buildroot}%{_prefix}/lib/udev/rules.d/95-rtirq.rules
@@ -65,25 +64,7 @@ install -D %{SOURCE1} -m 0755 %{buildroo
 install -D %{SOURCE3} -m 0755 %{buildroot}%{_sysconfdir}/pm/sleep.d/05-rtirq
 install -vD rtirq.service -m 0644 %{buildroot}%{_prefix}/lib/systemd/system/rtirq.service
 
-%post
-# only run on install, not upgrade
-if [ "$1" = "1" ]; then
-    /sbin/chkconfig --add rtirq
-#   /sbin/chkconfig rtirq on
-fi
-if [ -L /etc/rc.d/rc5.d/S81rtirq ] ; then
-    # update startup to new priority
-    /sbin/chkconfig --del rtirq
-    /sbin/chkconfig --add rtirq
-fi
-systemctl enable rtirq.service
-
 %preun
-# only run if this is the last instance to be removed
-if [ "$1" = "0" ]; then
-    /sbin/chkconfig rtirq off
-    /sbin/chkconfig --del rtirq
-fi
 systemctl disable rtirq.service
 
 %clean
@@ -92,17 +73,23 @@ rm -rf %{buildroot}
 %files
 %doc LICENSE
 %config(noreplace) %{_sysconfdir}/sysconfig/rtirq
-%{_sysconfdir}/rc.d/init.d/rtirq
 # udev and power management
 %{_prefix}/lib/udev/rules.d/95-rtirq.rules
 %{_sysconfdir}/pm/sleep.d/05-rtirq
 %{_bindir}/rtirq-udev
+%{_bindir}/rtirq
 %{_prefix}/lib/systemd/system/rtirq.service

That part looks good, you just need the new systemd scriptlets:
--
# This is actually needed for the %triggerun script but Requires(triggerun)
# is not valid.  We can use %post because this particular %triggerun script
# should fire just after this package is installed.
Requires(post): systemd-sysv

...

%post
%systemd_post rtirq.service

%preun
%systemd_preun rtirq.service

%postun
%systemd_postun_with_restart rtirq.service 

%triggerun -- rtirq < 20130402
# Save the current service runlevel info
# User must manually run systemd-sysv-convert --apply rtirq
# to migrate them to systemd targets
/usr/bin/systemd-sysv-convert --save rtirq >/dev/null 2>&1 ||:

# Run these because the SysV package being removed won't do them
/sbin/chkconfig --del rtirq >/dev/null 2>&1 || :
/bin/systemctl try-restart rtirq.service >/dev/null 2>&1 || :

--

Then, if the Fedora Jam folks have moved over to the new preset logic [1] making rtirq start by default on that spin is as easy as adding a line to a file.

[1] http://www.freedesktop.org/wiki/Software/systemd/Preset/

rtirq-20130402-4.fc19 has been submitted as an update for Fedora 19.
https://admin.fedoraproject.org/updates/rtirq-20130402-4.fc19

rtirq-20130402-4.fc19 has been pushed to the Fedora 19 stable repository.  If problems still persist, please make note of it in this bug report.