The second argument of Position is a pattern to look for
?Position
Position[expr,pattern] gives a list of the positions at which objects matching pattern appear in expr.
Position[expr,pattern,levelspec] finds only objects that appear on levels specified by levelspec.
Position[expr,pattern,levelspec,n] gives the positions of the first n objects found.
Position[pattern] represents an operator form of Position that can be applied to an expression. >>
In your Association the pattern {16505, 91521} does not appear
Note I left out the quotation marks that you had in it since the association you give as an example has lists of integers on the right hand side:
In[1]:= temp = <| 234 -> {16504, 16505}, 456 -> {91521} |>
To get what I think you are after you need to put Alternatives in the second argument of Position, not a list of values, as in
In[2]:= Position[temp, 16504 | 91521]
Out[2]= {{Key[234], 1}, {Key[456], 1}}
