If you copy and paste US-format dates (mm/dd/yy) into a Smartsheet while your personal settings are English (UK) (and presumably other Anglophone options), the data will retain the US format for all dates below 13. Where the date is 13 or more, Smartsheet will automatically transpose the format to dd/mm/yy. This can be confusing.
I suggest two work-arounds.
Either:
1. Convert all the dates to the required dd/mm/yy format before you paste them into Smartsheet;
or
2. Change your personal settings to English (US), then paste in the US-format dates, save, then change your personal settings back to English (UK).
I guess the same applies (in reverse) to anybody pasting UK-format dates into their US-format Smartsheet.
Smartsheet say this is expected behaviour, so don't expect it to change any time soon.