Yes — that behavior is likely normal for this particular Tamron 70-200mm f/2.8 Di LD Macro (N001). It’s widely regarded as a relatively slow autofocus lens, so hunting or lagging focus can happen, especially in challenging situations like live music venues with low light and low contrast.

Changing focus settings may help a little in some situations, but the lens itself is known more for slower AF performance than for fast subject tracking. If you’re seeing focus bounce in and out, that’s consistent with its reputation rather than necessarily a compatibility problem with the D5300.