Is it necessary to distinguish inclusiveness in possessive markers?

Merhaba!

My conlang Tsaan /tsa:n/ has a pronoun system like this:
I
we (excluding the listener)
we (including the listener)
you
yall
he/she
they(?I'll think about it)

Is it necessary to include the feature of inclusiveness in possessive markers? So
do you say 'That's our-EXCL new house' vs. 'That's our-INCL new house', or is
that necessary? Could one tell from context the intended meaning? In this case
it's pretty obvious, but are there cases where context cannot be used to
determine the meaning?

--Trebor

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