This is what I got on my S4 international with CyanogenMod Rom 4.4.4 nightly build from 2015-06-14 with an on demand cpu governor.
On this test I opened the coursera app then browsed for some section. So it's a typical one touch action what you're going to see here.
So I did an adb shell and started tinkering. I found nothing usefull on /proc/cpuinfo, then I headed for dmesg.
Note: to run dmesg you need to be root.
Note 2: dmesg -c clears the buffer, so you can be sure you won't see the same thing twice. It helps because it's kinda confusing because it's going up and down all the time.
root@ja3g:/proc # dmesg -c | grep -i clock
<6>[74960.230777] B0 23943 PVR_K: SGX change clock [177] Mhz -> [266] MHz req [266] MHz / M[800] / B[0]
<6>[74960.330888] B0 23943 PVR_K: SGX change clock [266] Mhz -> [350] MHz req [350] MHz / M[800] / B[0]
<6>[74960.431147] L0 23943 PVR_K: SGX change clock [350] Mhz -> [480] MHz req [480] MHz / M[800] / B[0]
<6>[74960.630002] L0 23943 PVR_K: SGX change clock [480] Mhz -> [350] MHz req [350] MHz / M[800] / B[0]
<6>[74960.930147] B0 23943 PVR_K: SGX change clock [350] Mhz -> [266] MHz req [266] MHz / M[800] / B[0]
<6>[74961.229909] B0 23943 PVR_K: SGX change clock [266] Mhz -> [177] MHz req [177] MHz / M[800] / B[0]
<6>[74962.330790] L0 23943 PVR_K: SGX change clock [177] Mhz -> [266] MHz req [266] MHz / M[800] / B[0]
<6>[74962.734868] L0 23943 PVR_K: SGX change clock [266] Mhz -> [177] MHz req [177] MHz / M[800] / B[0]
My interpretation of the data is the following:
I touched the screen and it started transitioning about 74960.230777 seconds from boot, when the governor kicked in.
It went from min frequency (177) to 266 then 350 and finally 480 Mhz at 74960.431147 seconds, meaning about 200 ms after it started throttling up.
Then it started slowing down on 74960.630002, reaching minimal speed on 74961.229909 (600 ms later). I have no clue what happened after that, probably it was still building something on the screen and throttled up and down again.
I don't even know if this makes sense, I have 4 slow processor and another 4 fast/power hungry processors, maybe I should run some heavy lifting tasks to be more sure of what happens.
It's funny though to notice that even incoming unread hangout text messages make a small bump from 177 to 266 to 177 MHz.