The 2013 came with the newer model battery charge controllers. If it is the one that came with the TT it should be no issue.
I googled your year/model and came up with the specifications. It has a 90 amp battery charge controller which is plenty of power for your batteries. I would just monitor it the first time you use it. Also make sure your batteries water level is above the battery plates. My TT only came with a 45Amp unit, and before going SOLAR it had no problems keeping the batteries fully charged.
Just remember do not let your battery voltage go below 12 volts, as that it the 50% level.
See if you can get the model number from the charge controller. These controllers are controlled my a micro controller that times the different charging modes and will not over charge your batteries.
Here is the link I got the information from
2013 Jayco Eagle Premier 343RKTS Trailer : Reviews, Prices and Specs : RV Guide
2013 Jayco Eagle 284BHS
250Watt Grape Solar Panel, MorningStar MPPT 60 Charge Controller
1500 Watt Ramsond PSI, 2 Trojan T145 Batteries (260Ah)
2 - AirSight Wireless IP Cameras (used as rear view cameras)
EnGenius WI-FI extender, D-Link wireless (n) modem
MagicJack Internet Phone
2012 Ford F150XLT, EcoBoost w/3.73
157" Wheel base, HD Towing Package
Our Solar Album http://www.jaycoowners.com/album.php?albumid=329