Tophat uses Botwie (or Bowtie2) to perform alignment. Then, it looks down to the unmapped reads and tries to align them using information about splicing junctions.

Tophat does not map reads. It relays and control bowtie to do the mapping

An initial mapping is done with the entire and unmodified reads using bowtie

Then, Tophat takes the control again allowing you to splice or break the unmapped sequences into fragments (you decide the size of them..), and then it will use bowtie again to map these new (spliced) pieces in order to fit them into different putative exons or regions. TopHat will take care of everything including statistic and what has been done and how

Tophat2 uses bowtie2 to align spliced reads, since bowtie2 by itself won't align them.