How can I get plastic wall anchors to work with a tile wall?
Drywall anchors depend on making the hole a little bigger as they are inserted.  This is a good thing, because drilled sheetrock holes may have chunks missing and the gypsum is not necessarily compacted.  Inserting the anchor compresses the surrounding gypsum and makes it stronger.

Tile is, of course, not flexible or malleable, so you'll have to drill a slightly larger hole through it.  To get maximum holding power, use two bits.  The smaller one all the way through, followed by the larger one just through the tile with minimum drywall contact.  Without knowing which kind of anchor and its size, I can't tell you what size bits to use.  I would experiment by trying 1/64 inch larger increments until the anchor slides through normally.