Update Slow Time Club to the latest version first. A recent update fixed a problem where a limit you'd changed to Weekday or Weekend could still block apps on other days. Find Slow Time Club in the App Store and tap Update if you see it.
Two things that surprise people
Each app gets its own time. A 30-minute limit on three apps means 30 minutes for each app, not 30 minutes shared between them.
Earlier use today counts. If you set up a limit in the afternoon, the time you spent in that app in the morning counts too, so it can be blocked straight away.
If it's still firing at the wrong time
Check today is in the limit's schedule (Everyday, Weekday or Weekend). To see which days count as weekdays and weekend, tap ⋯ on a limit, then Edit limit, and look at the schedule step.
Make sure Screen Time is recording: Settings → Screen Time → App & Website Activity should be on.
Compare with Apple's own numbers: Settings → Screen Time → See All App & Website Activity. The App Limit card in Slow Time Club shows the same usage Apple reports. If Apple's number is high too, that's the count iPhone is using.
If you have an iPad or Mac on the same Apple Account, try turning off Share Across Devices on every device: Settings → Screen Time → Share Across Devices.
Save the limit again. Tap ⋯ on the limit, then Edit limit, go through the steps and tap Set Limit. This registers the limit with iPhone afresh. If you've already used up today's time, the app locks again shortly afterwards.
Restart your iPhone and update iOS: Settings → General → Software Update.
A That's it for today screen stays up until midnight, when each app's daily time starts again.
For anything else, try Blocking isn't working: start here.
Why this happens
Sorry about this. iPhone counts your usage and tells Slow Time Club when an app reaches its limit. Sometimes that message arrives late, or not at all, often when the phone is low on memory. iPhone can also count too much, for example by adding time from your iPad, or by counting a website and Safari separately. Apple knows about this. We can't see the count ourselves, so we go by what iPhone tells us.
Related: App Limits: how do I set a daily time budget for an app? · How do I change or remove an App Limit? · My screen time looks wrong or too high
Still stuck? Contact us from Profile → Help and Legal → Contact support and include your User ID (Help and Legal → User ID).