The short answer
A mechanical watch doesn't necessarily keep exactly the same time sitting on a timegrapher as it does when you wear it.
That's normal.
A mechanical movement is affected by position, temperature, activity and the amount of power stored in the mainspring. During an ordinary day all of those things change.
This is why a single timegrapher reading isn't the same thing as predicting exactly how many seconds your watch will gain or lose tomorrow.
From the bench
A timegrapher is an extremely useful diagnostic tool. It allows a watchmaker to observe things such as the movement's rate, amplitude and beat error.
But it observes the watch under controlled conditions.
Your wrist is anything but controlled.
During the day the watch might spend hours dial-up, periods vertically on its side, and constantly move between different positions as you go about normal life.
Gravity affects the balance differently in those positions, and small differences between them are perfectly normal in a mechanical movement.
The state of wind matters too. A fully wound mainspring delivers power differently from one approaching the end of its reserve, and amplitude can change as that stored energy reduces.
A vintage movement adds another dimension. Components which have worked together for decades develop their own characteristics. A healthy older movement can therefore perform very well without producing identical figures in every position.
This is why, at the bench, we don't judge the health of a vintage watch from one attractive number.
We look at the movement as a whole.
What we recommend
Judge a vintage watch primarily by how it behaves in real use over several days, rather than repeatedly comparing it with a phone or atomic clock over a few hours.
If it consistently gains or loses a similar amount each day, a watchmaker may be able to improve its rate through regulation.
A sudden or substantial change is more interesting. If a watch that has been running consistently begins gaining or losing considerably more time, its power reserve changes noticeably or its behaviour becomes erratic, that can justify inspection.
And don't be alarmed if the timegrapher says one thing while your wrist produces something slightly different.
They're measuring two different circumstances.
The timegrapher tells us about the movement. Your wrist tells us about the watch.