ts is one of the many auto-expanding code snippets R Studio provides to get you started. Here's what the snippet definition looks like by default:
snippet ts
`r paste("#", date(), "------------------------------\n")`
So really it's R + your computer's locale the C function ctime that's responsible for the date format
You can edit the snippet to have it generate any date/time format you like by going to Preferences > Code > look for the tiny button at the bottom of the pane that says "Edit Snippets...".
Admittedly, the snippet editing area could be easier to find!
Snippets are a lot of fun... go forth and wield this mighty new power 