Encontrarse a / con

Encontrarse a / con
 

Siempre me encuentro a los vecinos por las mañanas:

I think this one means that you see them from a distance, but you don't say hello. A translation might be:
- I always 'spot' my neighbours in the mornings.


Siempre me encuentro con los vecinos por las mañanas:

I think this one means that you see them, and that you also say hello to them i.e., you greet them. A possible translation:
- I always 'bump into' my neighbours in the mornings.

Clarification on this would be hugely appreciated.
Thanks in advance.

The explanations for the examples you gave are correct.
The 'encontrarse a' structure means seeing someone, maybe from a distance, but not stopping to talk with them. You spotted someone.
The intransitive construction, with 'con', means that you said something to someone that you saw. You're face-to-face.

I agree with Rusty, but I'll add a note:

In Mexican colloquial speech, "siempre me encuentro a mis vecinos" may include interaction between you and your neighbors (you may or not greet or talk to them), but you didn't plan that meeting; in this case, it simply means that you all leave your homes at the same time, and the coincidence makes you see one another. => I always see my neighbours / I always bump into them.

"Siempre me encuentro con los vecinos" may be a synonymous sentence, but depending on the context, you may have planned those meetings. => I always meet my neighbours (with a purpose) / I always bump into them.

Many thanks!