Answer: It really doesn't matter to the plant. If we're talking about organic mulches like leaves or bark chips, I have found it easier to plant and then come in with mulch to dress up the area. With the hot weather you're having in Houston, it is a good idea to get that mulch on right away.
This goes for all plants. The only exception being an early garden planting of let's say tomatoes, where you want the soil to warm early. In that case delaying mulch may be beneficial.
If however, you are planning on using a fabric weed block over the area, you may find it easier to lay the fabric and then cut holes for the plants. Remove soil from the planting hole and place it in a bucket. Set the plants and then firm soil around the plants and water in well. Then dress up the surface with decorative wood chips.
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