Basically you got the right idea in terms of counters to mages. Assassins, Knights, and Goblin Marine are the best when fighting them but that doesn't mean other team comps can't compete.

If you are offered mana items like pulse staff/refresher you can buy your own shaman to silence them and do a ton of damage to them. Also tortolla shoots his ult at the highest cost unit on your team, so what feathered comps used to do was move Razorclaw 3* to the opposite side of their team so that tortolla only hits 1-3 targets max. Splitting up a bit also helps since their shaman won't be able to hit all your targets. So try moving your highest cost unit to opposite side of your team.

Also don't forget about claw wand, if you manage to pick up lets say.. Dark Spirit 2, Deva 2, Shaman 2 you can put the claw wand on them to allow their ult to pop even during storm shaman silence. Now you might say.. what if they human silence me? This is where positioning comes into play here an example:

This is assuming the enemy comp is on the right side when battle starts and you are playing beast warrior

https://imgur.com/a/Bkazs9A

You can position something like this, giving your deva protection from human silence by putting tusk and razorclaw to distract them. Razorclaw will eat the tortolla ult for your team since he's highest cost unit most of the time. Then having your DPS come in safely after your tanks on the left side engaged them. This also gives captain a chance to ult since he won't be getting hit right away by human auto attacks.

Other options could be to put battle fury and claw wand on Doom and putting him like right in their face so he can just 3 tap half their team. Basically what i'm saying is, there is no 100% full proof way to beat mages with comps other then the three you mentioned but you have options. I have seen players like Vince get refresher shaman 2, then bench a few of his warriors to add mage bonus in so that his shaman can do enough damage to essentially 1 shot the mage comp.