First off, I know this is an old post, but I still want to share the solution that I found to this problem.
Having the same issue with my android phone, still being able to connect to the internet, even though the Pihole was offline, and also not blocking adds in different apps on the phone.
The issue for me, was DNS on the phone.
First, I had to modify the Wi-Fi network witch I am connecting to, from Dynamic to Static, to be able to change DNS manually.
Then I set DNS1 to the Pihole IP, and DNS2 to 0.0.0.0, witch did not work. The phone for some reason, just resolves a second DNS on its own, witch one I don't know, could be one of googles.
After a lot of grief, I finally tried setting both DNS' to the Pihole IP, and this solved the problem for me.
I hope this might help others, having this issue.