I have always found the time message next to the account name very useful. It usually answers the question "is my local email up to date". It is red if there has been a failure to sync, say because of poor or no connection, black otherwise. (Not sure if the red figure is the last successful sync or the first failed one - I suspect it is the former).
I see a cosmetic problem if the tablet has been turned right off (not just sleeping) for a while. When turned on again, initially it displays in black the time of the last sync, maybe several hours ago, just as expected.
But: If I tap the " refresh all", then all my accounts are refreshed, and new messages appear. The time does NOT change at this point. A cosmetic problem as it is clear the mailboxes have been refreshed at this time.
If I manually refresh again, usually no more new messages arrive, but the time is also updated, as expected. I have not checked positively, but I believe it updates also when the app triggers an update by itself, but if this is the first such update since powering up, the time does not change till next time around.
I have one account set to push, the others not set to push. All IMAP, and my version number is 1.4.0.53. Device is google nexus 10, android 4.4.4, kernel 3.4.39.gd52af31, build KTU84P.
It is cosmetic only, as it corrects itself within fifteen minutes, or after a second manual refresh, and seems not to affect function otherwise.
Thanks for this app - keep up the good work!