Again the old porblem of the difference between = and :=
f[t_]:=Get["filenam"] should be interpreted as
"when you call f[any single argument] it gets the file "filename"
the right hand side of the definition is evaluated EACH TIME you call the left hand side.
what you need is to change the definition of f to
What happened here that at the stage of definition the right hand side is evaluated and the contents of the file enters as the value associated with f[t_]