The record updates are only sent to the devices if the last sync date of that mobile user is BEFORE the Last Modified date of the record. Normally, if you update a field in the record it will be flagged for upload to the device. The exceptions are changes in roll-up summary fields and in formula fields. pointing to other records. The Last Modified Date would not be updated due to a change in a formula field or a roll up summary.
Behind the scenes formula fields aren't stored as part of the record in the database, instead they use logic embedded in SQL at query time (when the record is displayed), so the values don't actually persist in the database. Instead they're generated real time when the object is queried.
To send updates on these fields to the device, you can use a workflow or a trigger that changes an actual field value based on a known condition. This will update the Last Modified Date and trigger the record in the device to be updated on the next sync.