I think that your terminology may throw a lot of people off because the word phasing is usually reserved for haplotype phasing, i.e., the determination of the allele (maternal or paternal) on which a particular variant appears. Instead, I am certain that you refer to the type of phasing that occurs during sequencing-by-synthesis (SBS). Thankfully, I have a colleague who worked on the development of the Solexa technology (which was purchased by Illumina and eventually used in MiSeq and HiSeq), and s/he explained this to me.
During each cycle of sequencing in SBS, a single base is supposed to be added by polymerase to the growing double strand. Every now and then, more than 1 base will be added during the same cycle - this is Pre-Phasing. When no base is added (when it's supposed to be), it's called Phasing.
Although this can contribute to sequencing errors at every cycle, I don't believe that there is any data to say that it actually results in more indel calls. These types of errors will be isolated to single reads.
To answer your question more specifically, a level of correction does occur within the instrument whilst all of this is happening, and it's a mixture of both wet-lab and informatic 'tricks' that occur. Essentially, one can spike-in a PhiX control sample in order to assist in the detection of these errors and 're-calibrate' the reads as they are being sequenced. The instrument is capable of detecting these issues in the first place based on signal 'cross-talk', i.e., signal strength and the presence of two signals at the same cycle (when pre-phasing has occurred), or no signal (phasing). In the initial cycles, the sequencer may struggle to detect these errors; however, as these errors begin to grow as the run continues, due to the fact that each subsequent cycle is dependent on the fidelity of the previous cycle, the error will eventually be easily detectable and that's when the error correction will kick in.
For further reading, see Illumina's own technical white-paper on this: Using a PhiX Control for HiSeq® Sequencing Runs