It is unclear whether or not Varys trusts Tyrion; as we do not know the inner workings of Varys' mind, or his ultimate intentions... Yet. But it doesn't matter as Varys didn't have the opportunity to tell Tyrion, therefore the point of Varys trusting Tyrion is moot.
Little birds can only whisper so far
This is an interesting case, since after the events of A Storm of Swords
where Tyrion kills his own father, Tywin
Tyrion gets shipped off to Illyrio's manse in Pentos in a crate. This is all done very fast and Varys clearly has no time to tell Tyrion anything.
Whilst in Pentos, it is Illyrio who introduces Tyrion to their Targaryen alliance and "plans", he doesn't tell Tyrion of the full plans, but that may or may not have had anything to do with trust.
To tell or not to tell
Tyrion at this point is a broken man. He has been convicted of Regicide (which he happens to not have committed), and is on the run since
He's also drowning in a sea of wine. He most definitely is not in the right mind, nor is he himself.
Whether or not Varys and Illyrio (Vallyrio) trust him when he his sober, is irrelevant, since Tyrion is not going to be of much help, let alone be trustworthy in his drunken stupor.
Whet his appetite
You see, Tyrion has just lost his right to Casterly Rock, and Illyrio offers him a chance to win it back; this gets Tyrion going.
Once on his way, he slowly discovers that people aren't who they say they are and other mysteries, such as:
this very much intrigues Tyrion and his curiosity; he just can't help trying to solve things and to prove his intellect. Finally he finds out that
Young Griff turns out to be Aegon VI Targaryen (questionable, but that's a whole other kettle of fish).
aaaaaaaand he's hooked!
It's the journey, not the destination
So, Vallyrio are clever enough to know that Tyrion is an asset. He has proven his worth many times over:
- Successfully improving the cisterns and drainage at Casterly Rock
- Successfully evading the death penalty at the Eyrie
- Successfully cleaning up King's Landing whilst serving as The Hand of The King
- Successfully defending King's Landing against one of the most formidable forces to ever engage in war against the city, in The Battle of The Blackwater
Let alone all of his smaller triumphs. So they are ready to utilise him, and they know (especially Varys with his many one-on-one dealings with Tyrion) that he is very intelligent and capable of leading or at least advising the intendeds, but he has to be interested first! - hence the "journey" to discover the truth!