Plenty of phones running Tollgate also run Downtime, App Limits, a Focus schedule, or another blocking app. Mostly this is fine. Here is the honest compatibility table.
Coexist cleanly. Each system enforces its own rules, so whichever is stricter at any moment wins. During Downtime you may see Apple’s shield instead of Tollgate’s, and answering a toll cannot override a Downtime block, because Apple’s own restrictions outrank everyone’s. Outside Downtime hours, Tollgate operates normally.
Focus does not interfere with the shield, but it can interfere with the unlock notification, which is how the shield hands you back to your question. A Focus that silences Tollgate swallows that notification, and the unlock button will appear to do nothing. If you scroll under a Focus, add Tollgate to its allowed notifications. Full story here.
They use the same Screen Time machinery Tollgate does, and iOS allows several at once, so shields can stack: clear one app’s gate and find another’s behind it. Confusing, but not broken. If gates seem to fire at the wrong times, or clearing Tollgate’s toll does not unlock the app, another blocker is usually the reason. Try running one referee at a time.
If your phone has Screen Time restrictions managed by someone else, those outrank Tollgate the same way Downtime does. Also check Content & Privacy Restrictions, which can suppress third party shields entirely, covered in the shield checklist.
One Apple setting deserves special mention: Settings → Screen Time → Share Across Devices. With it on, usage from your iPad or old iPhone can leak into this phone’s count, making gates arrive early, late, or seemingly at random. If your gate timing feels haunted, turn this off first.