Records are flagged to be sent to the devices if the last sync date of that mobile user is older than the last modified date of the record. So if you directly changed a field in the record it would be flagged to be uploaded to the device.
Therefore, first make sure that the field officer has synced the device to get the latest information. Also remember to examine your drill down selections to validate you are comparing the same record. (This is one of many reasons why adding unique identifiers in the detail field is useful.)
Exceptions - Formula fields and Rollup Summary fields driven by other records
However, changes to formula fields won't trigger changes because if a parent record driving the formula field changes it is not counted as a change to the record itself because formula fields are calculated real time by the system when viewing a record.
This doesn't count as a modification. A process in the background calculates that total, but is not considered a System field update. Behind the scenes formula fields aren't stored as part of the record in the database, instead they use logic embedded in SQL at the time of the query, so the values don't persist in your records.
Therefore, System Modification fields/Last Modified Date would not show up for formula field/roll up summary or trigger unless it was actually modifying a field on that record.
If you create a trigger on Account which in turn affects the contact record, it will not change the Last Modified Date or System Mod Stamp.
Some customers have built Salesforce triggers that update child records when the parent record is changed.
A workflow that changes a field based on some condition should also work.