Delayed SMS for Text-Based Leads?

[expinch]

We seem to be getting leads delivered through SMS about 5-15 minutes after we actually receive the email notification that a message lead has come in. I know that you're supposed to respond to message leads within like 3 minutes (what I've read), but that seems impossible unless you're scanning email constantly.

Is this normal?

I have set up a Zap that scans our email and sends us an SMS immediately to try to increase our response time, but this just doesn't sound right.