tophat splits the reads, but still requires everything to match. You could have mismatches in the beginning or end, but these would be scored as M in the CIGAR string. You have to look in the MD tag for mismatches. Old tophat versions dont have the optional MD tag. You can generate it with samtools calmd.

You always need a reference sequence. You can use a junction file or a GTF file in addition to this. Tophat automatically tries to align reads that can not be mapped completely by aligning them in a split fashion, thus discovering junctions. You can turn this off, modify it with parameters or supply your own junctions. But you should also have a junctions.bed file in your output and see some reads with a CIGAR like 20M500N50M.