Two separate questions
Residency splits in two: where the agent’s own data lives (logs, audit, task files) and where model calls go (the provider’s servers). Both matter, and they have different levers.
The agent’s own data
Task files, logs and the audit trail stay in the infrastructure you control — your machine, your console, your storage. Keep them there: resist the urge to mirror logs to a third-party service without checking its regions.
Model calls
Every cloud model call leaves your geography to the provider’s region. The levers are: pick a provider with the region you need, minimize what you send (never paste more context than the task needs — also a cost lever), or keep the sensitive stuff entirely local with Ollama.
The local-model escape hatch
A local model answers the residency question by never asking it: prompts and outputs stay on the machine. The trade-off is capability and speed — the split-model pattern in cheapest LLM for agents sends only the hard steps to the cloud.
Document the answer
Write down where each data class lives and why — the same documentation discipline as the GDPR checklist. Residency questions arrive in contracts and audits; a one-page answer beats a scramble.