Yes, that is the default setting.
You can turn automatic downloads off:
Settings/iTunes & App Stores/
There is a list of items that will automatically download - Music, Apps, Booka & Audiobooks, and updates.
If you have new purchases, it will automatically download to your other devices.
Turn of the selections for anything that you don't want to automatically go to your other devices.
I THINK you would need to check that the settings are the same on your other devices, too.
You will need to manually delete the apps that you don't want on your iPhone.