As a general rule, putting wide tires on narrow rims can result in the inner tube not fully settling into the rim cavity as the tire is inflated. It becomes necessary to tug the valve out during the very first few strokes of the pump.
This because the air pressure pins the expanding tube to the inside wall of the tire. Then, as the tube expands into the rim cavity, the wall of the tube may not slide easily around the corner created by the outward-splayed tire sidewall. Next thin you know, the tube may rupture from localized stretching. A bigger tube helps a lot since it doesn't have to stretch so far, and talc may also help by easing the sliding.
CTL370 rims have shallow bead-retention "hooks", so are less aggressive at retaining the tire bead.
The important thing here is to avoid old tires with dry and more slippery surface rubber in the bead area. I've blown off wired and folding tires from these rims and both tires were aged. Always happened after heavy braking.
American Breezer mtb, American Classic ti road bike w/SRAM Force and XO, Crotch Rocket, SOMA 69'er w/XX-1 mtb, Handsome Shop Bike w/700c wheels. Bianchi SS 'cross
I've been using a Campy Record/Araya CTL-370 wheelset for almost 30 years and have mounted everything from 700x20 to 700x35 tires, including 700x32 and 700x34 'cross tires, without any problems (Currently running Schwalbe 700x35 Marathon Extreme's).