All, don't have the knowledge, hence a question

Situation :
- Myself and spouse are residents
- We own a house in NZ
- I am a Tax resident but spouse is not ( currently working in Singapore - hence work income from Singapore)

Question :
- Does it help applying for Tax residence for my spouse ?
- If yes, with DTA being in place with Singapore - what does it mean for us ? Do we file taxes in both countries and get tax deducted in both countries ? Then we look for Tax refund in NZ ? Cant really makes sense out of DTA and the procedure.

Any guidance would help.