After some brief conversations during consulting about how to construct interaction terms for multiple regression (and why centering variables beforehand is important), I put together a short demonstration of R’s default behaviour when using the built-in convenience functions (specifically *, but also applies to formulas that use ^).
The vignette is posted here: https://rpubs.com/mattsigal/reg_interactions
The short-version: *, when used with summary() does not center the variables, and so models will have issues with VIF. This can be avoided either by creating the interaction terms with scale() or looking at the effects using car::Anova().