Each Istari had a different mission?

[Rhod the Red]

so he would not use his voice intentionally to manipulate the people

That's speculation.

If we judge by how it performed in the chapter of
'The Voice of Saruman' it would have ideally
been used after Beren tells his servants to leave
so that Saruman's alone with him.

He wasn't 'good' then, he'd already said no
to an assault on Dol Guldor and if you check
the timeline at the back of TLotR he had already
searched the Gladden Fields, etc. Probably
already obtained the Ellendil Star from Isildur's
body. As well as at least got to the point of spying
on the Shire.

We don't know whether Beren saw the White Council
as allies. Presumably Beren could speak Elvish, like
all from the Numenorian line on Middle-earth. So it's
logical either Beren voluntarily gave him the keys to
Orthanc & Minas Tirith archives or he coerced him
when the opportunity came.