What you mean by “stored under the common date” is not clear to me. Could you elaborate on that?
by default, Apple Mail does not rename nor file nor create mailboxes (folders) using dates, absent some local scripting rules. Alternatively, rules running on your particular mail server and mail account can reorganize mail messages using vadious details.
If multiple mail clients are all showing a specific name or mailbox (folder) or such, then it’s somehow common, or happening in a common way. it’s probably then a rule running on one system that is managing the messages on the mail server and thus visible to all clients, replicated rules, or something running in the mail server.
But again, I’m not sure what you mean by that common date.
If the arrival dates on the messages are all getting changed, that seems most likely to be a corruption arising on the mail server.