Excellent point. In your contactor specs, you will find values of "Inrush" (or "Pull-In") and "Holding" (or "Sealed) VA. The Inrush value is what you need to be most concerned with, because if your TD relay contacts are not rated for that, they could weld shut. On your timing relay, the contacts will have a "Make" and a "Break" rating. Your contact Make rating must be more than the contactor coil Inrush current (convert from VA by dividing by 208V), the Break rating must be more than the contactor Holding current too, but that's rarely an issue.
View attachment 13341
Contact ratings: Make = 15A, Break = 1.5A
Example:
100A NEMA Size 3 contactor, coil inrush = 660VA / 208V = 3.17A, no problem for this timer (but would be for one rated only 3A)
600A NEMA Size 6 contactor, coil inrush = 4860VA / 208V = 21.44A, big problem