Jetstar Transit Connection with Tiger in Changi?

Both a budget airlines, and would likely be opting of out interline arrangements which is costly for them to provide. The airport counter staff may give you the wrong info and you will be traveling without your bags. I suggest you clear immigration and take your bags with you. The wait in between is bearable. There are comfortable places like Starbucks you can relax at while surfing at the airport. The budget terminal is quite bare so don't go there until you are ready to check in. There is a free bus taking you to the budget terminal. Check the timings. Not sure they operate after 12 midnight.