Well, I think the term cycling has been misused in this case. The poster doesn't mention ammonia, just algae. A properly done water change (match salinity, temp, ph, don't leave the LR exposed to air for more than a few minutes, etc) of even 100% should not affect the nitrogen cycle too much.
What can happen when you do a large water change is that some nutrients/minerals/metals that are normally kept at a pretty depleted level by the existing algae and/or other photosynthetic creatures gets a big boost, brought in by the new water. Normally this is associated with using tap water, or less than perfectly clean RO water, but it could even be the salt mix. This sudden influx of whatever it is that is limiting algae growth allows for an algae bloom.