As this is a mixed class (Y on EI/PY on SQ) /mixed airline (EI/SQ) booking, SQ's systems will be challenged. While SQ can sell the ticket upfront (somewhat impressive given SQ's IT), their upgrade engine is clearly using an alternative source to calculate fares.
As for a potential upgrade offer from SQ, this will be at around 72 hrs before departure. Of course, whether you receive an offer depends entirely upon availability in the next class.