no tensioner on aux belt unless you have air-con but apart from that, agreed.
oops most likely is water pump but you need to eliminate the alt first then add water soluble oil or brake fluid to coolant if the engine is quiet the next day the pump bearings are rusty and the pump needs replacing before it takes out a head gasket... last option is cam belt tensioner they are well reliable
the alt is run overspeed and gets a lot of spray if the undersized is missing forcing a hot alt is lethal. ..