In the US our actual vote is secret and anonymous, so it is possible to hide who you “pull the lever” for. When you vote in the primary however, (in most states) it is recorded which party’s primary you choose to vote in (but again your actual vote is secret) . This is a matter of public record (don’t ask me why) and campaigns use that info to target people based on their likelihood to vote for them. So if OP chose to vote in the Dem primary, their name would be on record as having participated in that Dem primary, and the local/state/national Democratic Party probably would have sent campaign materials to their address (not like thank you notes, but more like ads for Dem candidates and causes), and their family may have deduced that they had an “outsider” amongst them. Another scenario is that OP may have just been honest with them when they asked.

Reminder to check snopes before believing random internet factoids:

https://www.snopes.com/fact-check/amazon-spray-boxes-chemicals/

Nashville TN suburbs and here are my walking distances:

To the nearest convenience store: 6km
To the nearest chain supermarket: 11km
To the bus stop: 6km 
To the nearest park: 4.1km
To the nearest big supermarket: 12km
To the nearest library: 13km
To the nearest train station: 25km