It was my understanding that the new 510 batteries that come with the 510T need a different charger (the one that they come with) that previous 510 batteries. So, unless you have a 510 charger for the previous style, then you would need to get the new 510t batteries to be compatible with the charger that they came with. However, when I looked it up on LiteCigUSA (where I bought my 510t attys and tanks), and read the description on the starter kits, it didn't say anything about this. Where I heard about the difference in chargers was in the video posted about a month ago on ECF that was an early review of the product (by Vermont Vapors).
http://www.e-cigarette-forum.com/forum/vermont-vapor/173224-demo-new-510-t-tank-system.html
When looking at the starter kit info on vermont vapor's site, it doesn't say anything about the batteries needing a different charger than previous 510 batteries.
Since I already had 510 threaded batteries, the charger was not an issue for me - I just bought the tank attys and tanks. It is a nice set up. Has slightly better flavor than the eGo tanks and don't seem to lose as much juice to leaking from the tank into the atty (although that was never a major problem for me with my eGo tank system. Only with those tanks that have been removed/replaced a bunch of times start to lose more juice in the atty. When that happens I just use a fresh tank). I haven't used my new 510t system enough to determine if this plagues this system as well.
But, that is for charging only. A regular 510 battery has the same 510 threads and will work with your 510 tank attys.
Since I don't have the new batteries, I can't say for sure about the charger required. I noticed that neither VT Vapor nor LiteCigUSA sells a special 510t charger or 510t batteries. My gut says that the initial review video may have been incorrect that they require a different charger than other 510 batteries. I think to be safe (unless someone posts later) you could email the vendor that you purchased your 510t from and make sure that the charger you got with your 510t system will charge other 510 batteries. Exception - if you upgrade to a Riva/eGo battery, even those are 510 threaded, they require a different charger (or adapter - but the charger is only about $2 more than the adapter. Better to have the charger IMO. You cannot charge an eGo/Riva battery on a 510 charger and cannot charge a 510 on a Riva/eGo charger - at least not w/o the adapter.