There’s a 30 - 60 minute time gap from the reply being received to it showing up in the master inbox.
This time gap is maintained to ensure clean connectivity amongst your email accounts. Short and repetitive access may flag your account for automation.
Most emailing tools don't provide webhooks for replies, e.g. (Outlook, Gmail, and Zoho), and as a result, we need to maintain sustained access to ensure we can capture replies.
With that said, there will not be a moment where a "follow-up" is sent without looking for a reply because right before a follow-up email is sent to a lead, our engine ensures there are no replies that were received in the "30-60" minute interval.
So your automation is always safe and top-class.