Civic's have a overall tyre diameter of 575mm
Vitz's have a overall tyre diameter of 583mm
Meaning that the vitz requires a tyre 8mm or 1.39% larger than the civic.
Anywhere between -1.5% and +1.5% s acceptable enough to not interfere with your speedometer so you should be fine.
What size tyres are you getting on the rims you are planning on buying?