I don't believe in the type with "tree" behind Minerva: the supposed "tree" is just her aegis with snakes emerging from it.
RIC 1243's source for the variant with "tree": J. Schulman Sale 1923, Vierordt Collection, lot 1611, not illustrated: "derrière Pallas une arbre morte, manque à Cohen". I think the tree was called "dead" because it had no leaves, just branches: but those supposed branches are just the snakes emerging from Minerva's aegis.
This is quite a common reverse type on Roman coins, especially of course under Domitian, and it never had a "dead tree" behind Minerva, just her aegis with snakes emerging from it.
This was clearly Strack's opinion also. He doesn't actually discuss the Vierordt coin in his appendix of rejected coins, but in his concordance he says RIC 1244 is equivalent to "(962)", that is his 962 misdescribed. Schmidt-Dick correctly omits this supposed variant from her Typenatlas, type f7B/01, though she does not discuss the matter as far as I can see. Unfortunately Strack's dismissal of the coin was not taken up by Mattingly in BMC 1776 note, where the Vierordt coin with "tree" is accepted as a true variant.