What do Illumina HiSeq/MiSeq paired end reads look like?
Where the reads found in R2 are the reverse complement of those found
  in R1.


This statement seems incorrect.

Paired-end reads comes from opposite ends of a fragment (you could learn the reason it happens from Illumina's video). If insert size is 150bp, read length usually is ~60bp as quality score after 60th bp is unacceptably low. In this case, R1 length is ~60bp, and it is 5'3', R2 length is ~60bp, and it is 3'5'. When a number of reads are enough to cover the gap, they form a contig.

Here's an illustration from Illumina's website: