Yes, that could very well be the conflict. Running “dmesg” after trying insmod on the target may offer additional clues.
I tried adding that module as well, and in my case it's built for ARMv7. I guess that it's key that you run the “make xconfig” (or menuconfig) step with the right cross-compiler settings as well:
env PATH=$PWD/../android-ndk-r6/toolchains/arm-linux-androideabi-4.4.3/prebuilt/linux-x86/bin:$PATH make -j4 ARCH=arm CROSS_COMPILE=arm-linux-androideabi- xconfig
If that turns out to be your problem, I'll update my guide to make this explicit.
No, a “make modules_install” is not required to use the module.