Were there peacekeeping forces he could rely on? If so, would they be from the capital or the province he's administrating? Were there documents he could show to someone upon arrival at his district to prove that he's operating on the authority of the emperor? Whom would he show them to?
To clarify, let's say Tang era, in a provence that's far from the capital, but not quite a frontier. Please tell me if I'm making any incorrect assumptions here, my knowledge of the time is more cultural than political.
During the Tang era, the military itself was administered through the Fubing system, which put a lot of power in the hands of regional generals, but most towns had militia in varying states of readiness. You're not going to be seeing troops from the capital anywhere but the capital.
If anyone has a better answer, go ahead, but I don't like seeing posts go unanswered, so I'll give it my best shot. High ranking appointments (county and above) had to be made by the Emperor himself, so the current holder of a post would probably get a letter from the capital at the end of his three year term telling him of his replacement, who would be carrying a badge to let you know he's legit.
As for day to day duties, the overwhelming workload of county magistrates was acting as a judge, settling disputes too serious to be left to village elders. Magistrates would investigate crimes, interrogate witnesses and suspects, and write up a formal decision upon receiving a confession, which they could extract through caning. This decision could be appealed to the prefect if there was a fault in the magistrate's application of the Code.
Other duties included storing grain in case of famine, managing irrigation projects and conscripting labor for them, assessing property for tax purposes, updating the county gazetteer once every sixty years, and keeping the local militia ready.
What period you are really interested in is not the Tang but the Song and afterwards. While the Tang Dynasty had a relatively developed bureaucracy for its day, it was still dominated by familial lineages and non-imperial politics tended to be local. The civil wars at the end of the Tang, however, effectively wiped out the great families and, combined with the demilitarization at the foundation of the Song, meant that the new dynasty had to create an administration from scratch. And so they repurposed the examination system from being, essentially, a tool of distributing favor among a handful of Chang'an based families into a true meritocratic system of recruitment. In doing so they expanded the reach of the bureaucracy drastically, with all sorts of interesting cultural effects.
So anyway, to answer your question, it of course depends on where they are. But if you imagine a place in the heartland, day to day would largely be hearing cases and resolving disputes. This is actually something of a truism of all pre-modern government, as administrations tended not to separate judicial and executive power, and of course resolving disputes is largely what governments are for. But broadly speaking, the lowest level of imperial government was a county, which varied a lot in size (the boundaries often were determined by local politics) but were often fairly large and any conflict that couldn't be solved within a the local community would go to the official, so one who wanted to be industrious could keep pretty busy. But being in charge of the judicial functions also meant that they were in charge of crime investigation, and the inspector official is actually a pretty popular character in Chinese literature ("The Canary Murders" short story has some great examples).
Beyond this, officials were generally agents of the imperial administration and their duties were to fulfill this. This could mean ensuring that imperial dictates were fulfilled as well as conducting land surveys to determine questions of tax burden. They could also be in charge of infrastructure improvement. Broadly speaking, the sort of duties an official takes depends heavily on their inclination.
But of course not everything was the heartland, and particularly in the military districts duties could be very different. An official posted to, say, eastern Sichuan may largely be more concerned with banditry, ensuring the stability of the frontiers, handling the tricky diplomacy with the various "uncooked tribes" that may or may not legally be under imperial jurisdiction, ensuring relations between Chinese and non-Chinese did not erupt in war and, if they did, ensuring that the integrity of China's overwhelming force was preserved (they may or may not directly lead troops). China was as it is very big and very diverse, and so the challenges any one particular official faces would largely depend on where they were posted.
There is a wealth of good overviews on China, Fairbanks' China: A New History being the best, but a lot of my specific information regarding the dynastic differences comes from the Harvard's great History of Imperial China series. Specific administrative information is heavily drawn from William Rowe's Crimson Rain (he also has a more directly relevant saving the World that I have not read) and Richard von Glahn's Country of Streams and Grottoes.