Check the switches
Cloud switches
Ollama, LM Studio's Bionic and Jan can all use cloud models alongside local ones. In Ollama, cloud models end in :cloud. In the other apps, cloud providers are listed separately. Before any private chat, check the model selector. The providers' promises about not storing data may be sincere, but they are promises, not physics.
Search and tools
Web search sends your query to a search service, even when the model is local. Tool connections (MCP servers, plugins) can read files and reach the internet with the app's permissions. Turn off search for private work, install tools only from sources you trust, and use the apps' approval prompts.
The local server
All three apps can run a server so other programs can use your models. Normally it listens only to your own computer. Settings can open it to your network or beyond. Leave it closed unless you need it, add a password or key if offered, and never expose it to the open internet; unprotected AI servers are regularly found and misused.
Prove it offline
The simplest proof is physical: disconnect from the internet and do the task. If the model, the document chat and the answer all still work, they are local. Updates, crash reports and usage statistics are separate; check each app's privacy settings and turn off what you don't want.
If you had to prove to a client that their document never left your laptop, what would you show them?