What tools do you use for cross-browser testing?

They should have some kind of strategy. Perhaps a web-based tool like BrowserStack. Perhaps a VM based tool like Virtual Box. Perhaps different actual computers.
Part of the job of front end design is making sure things work everywhere they can (based on decided-upon support). You don’t have to love it, but you can’t hate it. “This right here, this is the job. What kind of work were you expecting?”