Roblox packages are versioned. You can configure them to auto-update but, they only update automatically when you open the place in Roblox Studio (I’m pretty sure…)
You can try using a Model owned by you or the group that owns the game you’re working on. Dynamically load that model using InsertService:LoadAsset or if it’s a MainModule ModuleScript use require(assetId). You’ll always get the latest version of some module, and this might suit your case better. Downside is that you may not have a copy of the module in the place while you’re editing it.
No workaround right now. Auto update will carry your packages around to other places but they won’t publish the place file itself. You actually have to go in and publish all places in the experience that use the package after updating it with or without auto update.
Had this same concern and we brought up internally during Accelerator. Not sure what will come of that feedback, a feature request might more strongly convey the issues with the current way of handling packages so that they appear in live versions right away.