There is a book called Experts on the Anti-Sicilian (2011) edited by Jacob Aagaard & John Shaw. GM Matthieu Cornette of France wrote some excellent chapters upon the so-called Modern (Tiviakov) Grand Prix which could have been a reasonably sized book on their own.
On page 337 he gave his options against 4...a6. In brief, he stated in the above-mentioned book that 5.d3 is his preferred move in this exact position, as well as he cited many transpositions after 5.a4 (leading to another line) and 5.Nge2 which can be met by 5...b5!? (instead of 5...Nf6 which transposes to the so-called main line). 5.Nf3 b5!? was reviewed, too..
The move 5.Bb3 was not considered (maybe that's why your opponent played it, after all), but can lead to another transposition, of course.
Imho, this "Modern" Grand Prix is very interesting, as well as not heavy on theory. So, that's why it drew the attention of so many correspondence and OTB players. Hence, the strategy!
Anyway, black has several continuations (including 4...a6) which are very good and give the second player a good game. White strategy here is the usual Grand Prix's strategy. Keep the white bishop alive if you can and start an attack on the black king after f2-f4 and so on. If not 3...Nd4 (which is the best continuation, imho), then the first player destroys the black pawns structure with Bxc6 before black can play Nge7 or Bd7, then plays f2-f4, d2-d3, Bc1-d2 and Qd1-e1-h4 with a possible attack on the kingside or Nc3-a4, b2-b3, c2-c4, Bc1-a3, Ra1-c1 to attack the black pawn on c5, all depending of black's continuations.
Nothing new under the sun..
Just to add that now I play this opening with white in my correspondence chess tries for the third time. One exciting victory for now, another one is cooking (I hope), while the third one...hmmm, black (a big name in the correspondence chess) played very, very interesting.. Even GM Cornette haven't considered such continuation. And I cannot say I have a good game, for now..