If it is normal or not depends on how much it is tangled. Brush it really well before you wash it and use a good conditioner, don't brush it when it is wet you'll cause breakage. Use a wide toothed comb. Did your stylist put a glaze on after the highlights? That helps smooth the shaft of the hair down and keeps it feeling smoother and untangled.

Normal

Your hair got damaged, all processing causes damage BTW. Your cuticle got roughed up. You need to deep condition with a protein pack (I use Joico K-Pak deep conditioner reconstructing treatment in the gold tube).

Is this normal? I have very fine, usually silky, hair. I just hit highlight and it looks in the dry side and is getting very, very tangled.