Dynamic Tree Marked Ancestor Queries
If you don't need deletions, I think the first part of Lemma 4.1 on page 349 of the following paper:

Jeffery Westbrook: Fast Incremental Planarity Testing. ICALP 1992: 342-353
  http://dx.doi.org/10.1007/3-540-55719-9_86

gives you a linear time algorithm for any sequence of operations consisting of constructing and marking the tree, as well as conducting nearest marked ancestor queries (i.e. the query time is amortized constant).