I've known about the VFTF for a few years and I've never heard of it applying to only one leg of a journey, unless the qualifying visa is single entry. In that case the restriction is that it can only be used to travel directly from that country to your home country via Singapore after it has been used.
Travellers with Single Journey Visas (SJV) may still be granted VFTF on the return leg of their journey (i.e. after the SJV is used and no longer valid), but you must:
- Travel directly from the country that issued the SJV, en route through Singapore, back to your home country
- Not have returned to your home country since you last used the SJV.
With respect to your multiple entry student visa, no such restriction exists. You can use it for travel as long as it still has one month before its expiry date.
The airline should not deny you boarding in this case. Timatic, the database which airlines use to verify passenger travel documents, states:
TWOV (Transit Without Visa):
Nationals of China (People's Rep.) and India with a
confirmed onward ticket for a flight to a third country
within 96 hours under the Visa Free Transit Facility (VFTF).
- have a residence permit issued by Australia, Canada,
Germany, Japan, New Zealand, Switzerland, USA or United
Kingdom valid for a minimum of 1 month from the arrival
- have documents required for the next destination.