Assuming they are low voltage lamps with a transformer the reason is...
tungsten filament when cold has v. low resistance, so on switch on a v.large current would flow until hot, when current drops to about 1/6th .
the makers of the transformer (which to keep siize/cost down is electronic type) protect it by letting power build up slowly until lamp warmed up,
so in fact the lamps don't just come on after a delay it's just you don't see light until that point.
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