When I was in Japan, I remember seeing products such as razors with Neon Genesis Evangelion on the packaging, which I found a bit weird, considering that it isn't something that (I remember) showed up in the show. I was wondering: is all/a vast majority anime/real life product placement done as a mutual thing as described in this question, or are there other agreements that real life companies and anime companies have in terms of representation?
This is simply merchandising, and it has nothing to do with the show itself. It's like being able to buy Tshirts, mugs, hand towels, baseball caps, etc with the name/logo/picture of a character/etc from a certain show. It's to make money from something other than DVD/BD sales or in the case of films, box office take.
In certain cases, there's a marketing collaboration. This is almost always a mutual thing, product gets a bit of marketing by placing the anime into its products (hand cream, champagne, eye drops, shaving razors, etc) and the anime gets a bit of marketing from the people who normally buy this stuff anyways. Depending on the specifics of the contract, there could payment for either the property or advertisement or in some cases, royalties.