I decided to work on my pronunciation and got some podcasts and Cambridge's "Pronunciation in Use". And all I get for my efforts is confusion.

Native speakers on that tapes pronounce "t" very clearly in some words like 'often', 'restaurant', etc. while I always thought it shouldn't be pronounced there.
I was tempted to brush it off as a 'British thing' but
a) these are training tapes and presumedly they are to demonstrate standart pronunciation,
b) on a podcast both Englishman and American said 'often' (with 'T').

I'm not going to change my habbits (yet ) and to say it the same way but WHAT'S GOING ON? I'm just curious. Is that an accent or it's common?