Wooden cabinet pulls with glass tile inlay

Okay, Nobody has answered you, don’t think that’s right, but I’ll try. What i expect is firstly, when you install the tiles the grout is still wet, which causes expansion in the wood for the period until the grout dries. Secondly you use grout to install the tiles just to get the texture the same. What I would rather tend to do is, rather glue the tiles in place. Once completely dry, then only i would grout a small quantity as possible. Just take note, in the kitchen, humidity is high so your wood will expand and contract greatly. Best bet would be not to grout at all or use an pvc glue to mix the grout so it has the flexible characteristics you need. That might work.
Hope this helped, rather late than never.

-- An unfinished project makes great firewood for winter!