I am still playing with my process a bit for making and timing my starters. However, what works me now is to pitch my yeast cold. I whirlpool chill using ice, so my wort gets down to 40-45 F. This lets me dump the cold break before going into the fermenter. I also crash my yeast starter in the fridge a day or two before brew day so that I can dump the liquid and just harvest the yeast. Since both are cold, I just pitch and let them warm up to ferment temperatures together. I have not noticed an increased lag time; if anything, the lag time is decreased.
Often with microbes, the temperature differential is as or more important than the absolute temperature. I believe them sensing increasing temperature over a wide range in a sugar rich environment impacts them more than whether you ultimately hold at 67, 68 or 69 F (or wherever you ferment) in terms of progressing through the lag phase and initial growth phase.