As your are coming in as a tourist from Aus, you will be given a 30 day SVP. Once here you can then go to MOM and apply for an LTSVP (you may need your partner as well - for sponsorship) but may have to wait until his EP has been processed and obtained - inside of a week. As far a immigration, you probably won't even be asked why you are here. Both you and your s/o will arrive the same way, on SVP's. He won't received his EP until he is physically here in Singapore even though he may well have an Approval letter. ICA does not issue EP's - only MOM. However, LTSVP's are under the purview of both both but the types of LTSVP's are much different.
The link below will give you the information you need for the LSTVP application that is suitable in your instance (via MOM).
LTSVP
There is no need to "lie" to the immigration officers. If they ask, just tell them you are planning to apply for a LTSVP through your s/o's sponsorship. Don't worry so much. You can also apply for a 90 SVP online after arrival here as well to buy yourself more time.
sms
NB: I'm actually just an opinionated ole farmboy who says it like I sees it. I bark but don't bite!
