On 6 month probation in Florida for non-alcohol related reckless driving. I received a dui on Saturday in Tennesse, where I currently reside. I am only on mail in probation. What should I do to handle this with my probation officer in Florida? It is a Saturday and they are closed until Monday. Or, do I not do anything?

So you "think" you have a probation violation with this dui? You went to court and plead right? Your probation status should have come up at that point. Although since they are in different states, that might not be the case. You're on mail in probation so they may not even find out about it. However, this doesn't mean they can't. You have to weigh your options here. You can call them, let them know, and more than likely have your probation revoked. Or you can avoid calling them on the chance that they don't find out. No one can make that choice but you so don't take this as legal advice or personal advice.

The police here didn't even know I was on probation. Can Florida force me to jail time there too?

Any police contact and any ticket or arrest has to be reported to your probation officer. Failure to report this is a very serious violation. Actually the Probation Officer may consider not telling him, worst than the actual offence.

But yes, this is a violation of your probation and they can put you in jail over it.
If you do not tell them, when they look up your record prior to being taken off probation, you will be arrested ( almost positive of that)