Before the military ventures you mentioned, Dioclectian was actually in charge of border defense in Moesia (along the Danube near the Black Sea), which is where he would have initially made a name for himself as an officer. Then there was a legionary revolt in 282, during which Carus was elevated to imperator. He went off and fought against the Persians, then died in 283, but not before elevating his sons, Carinus and Numerianus, to the rank of Caesar. Diocletian clashed with Carinus at Moesia in 285 in the Battle of the Margus, in which Carinus died. After his brother, Numerianus, died Diocletian floated to the top of the food chain, so to speak. Aurelius Victor actually claims that Diocletian killed Aper, the Praetorian suspected of having killed Numerianus:

"And so Valerius [Diocletian] in his first speech to the army, having drawn his sword, gazing at the sun, swore that he was unaware of the plot to kill Numerianus and that he had not desired power. Then he sunk his sword into Aper, who was standing next to him. Aper's treachery, as I explained above, had led to the death of this good, eloquent youth, who had also been Aper's son-in-law. Pardons were then given to the rest and nearly all of the enemy soldiers were retained and a very distinguished man by the name of Aristobulus was placed in charge of the praetorian guard for his services. This action was new and unexpected within human memory, namely that no one in the civil war was robbed of their fortunes, fame, or dignity; for we rejoice when a civil war is conducted very dutifully and with mildness, and a boundary is observed in the case of exile, proscription, and even in the punishments and executions" (Aur. Vic. Caes, 39.13-15).

You're right that he skirmished with the Sarmatians, but I believe it was around 285, not 294-296 (if I recall correctly from Southerns' The Roman Empire from Severus to Constantine). After that, there are a few throwaway lines from primary texts of Diocletian fighting battles at the same time Carausius was causing Maximian issues in the West (c. 286-293), which Eutropius describes here:

"At the same period a battle was fought by Constantius Caesar in Gaul, at Lingonae, where he experienced both good and had fortune in one day; for though he was driven into the city by a sudden onset of the barbarians, with such haste and precipitation that after the gates were shut he was drawn up the wall by ropes, yet, when his army came up, after the lapse of scarcely six hours, he cut to pieces about sixty thousand of the Alemanni. Maximian the emperor, too, brought the war to an end in Africa, by subduing the Quinquegentiani, and compelling them to make peace. Diocletian, meanwhile, besieging Achilleus in Alexandria, obliged him to surrender about eight months after, and put him to death. He used his victory, indeed, cruelly, and distressed all Egypt with severe proscriptions and massacres. Yet at the same time he made many judicious arrangements and regulations, which continue to our own days" (Eutr. Brev. 9.22-25).

In fact that mention of Alexandria is what you referred to you in your question, OP. The problem we have here is that the Tetrarchy performed its duties very well in that it split up the administrative and military efforts into four distinct sections, creating a multiplication of expenses, taxation, and bureaucracy. Aurelius Victor comments on just that:

"At the same time, the Persians were harassing the East, while Julian and the Quinquegentana were violently disrupting Africa. Moreover, near Alexandria in Egypt, a man named Achilleus had assumed the insignia of kingship. For these reasons, they called Julius Constantius and Galerius Maximianus (who bore the nickname Armentarius [sheepherder]), and made them Caesars by marriage. Constantius was given the step-daughter of Herculius, Galerius the daughter of Diocletian; their earlier marriages were dissolved, just as Augustus had done the same thing in the case of Nero Tiberius and his daughter Julia. Illyricum, admittedly, was their homeland: naturally they were uncultured, nevertheless because of their experience of the hardships of country and military life, they were the best men for the republic. Therefore it is a fact that revered, intelligent men are made more quickly by the experience of trouble; on the other hand, those having no share in tribulations, as long as they judge everyone else by their own resources, their judgement is less sound. But their harmony gave excellent proof that talent and good military discipline, as it had been established by Aurelius and Probus, is almost enough to constitute good leadership. Finally, they looked up to Valerius as a parent or like a great god. The nature and importance of this has been revealed from the founding of the city down to our own time by the crimes of relatives.

"And because the pressure of the wars, which I wrote about above, was increasing rapidly, in a four-part division of power, all the lands of Gaul, on the other side of Alps, were handed over to Constantius; Africa and Italy were given to Herculius; the land from the border of Illyricum all the way to the Sea of Pontus was given to Galerius; Valerius retained the rest of the empire. Finally the great evil of taxes was inflicted upon part of Italy. For although he was pursuing a reasonable policy of equal revenue collection everywhere, a new law was introduced for taxes, by which the army and emperor, who are present always or most of the time in Italy, would be sustained. Admittedly the tolerable moderation of those times had advanced to the ruin of these days" (Aur. Vic. Caes. 39.22-32).

The way the Tetrarchy was structured makes it somewhat difficult to pin down which emperor was present for which battle. The clashes with Persia in the mid 290s, for example, we know involved Galerius, but we don't know if Diocletian was also present. Of course, Galerius suffered a defeat at the hands of Narseus, so politically Diocletian wouldn't have wanted to associate his name with those battles. As Eutropius puts it:

"Galerius Maximian, in acting against Narseus, fought, on the first occasion, a battle far from successful, meeting him between Callinicus and Carrae, and engaging in the combat rather with rashness than want of courage; for he contended with a small army against a very numerous enemy. Being in consequence defeated, and going to join Diocletian, he was received by him, when he met him on the road, with such extreme haughtiness, that he is said to have run by his chariot for several miles in his scarlet robes. But having soon after collected forces in Illyricum and Moesia, he fought a second time with Narseus (the grandfather of Hormisdas and Sapor), in Greater Armenia, with extraordinary success, and with no less caution and spirit, for he undertook, with one or two of the cavalry, the office of an scout. After putting Narseus to flight, he captured his wives, sisters, and children, with a vast number of the Persian nobility besides, and a great quantity of treasure; the king himself he forced to take refuge in the remotest deserts in his dominions Returning therefore in triumph to Diocletian, who was then encamped with some troops in Mesopotamia, he was welcomed by him with great honour. Subsequently, they conducted several wars both in conjunction and separately, subduing the Carpi and Bastarnae, and defeating the Sarmatians, from which nations he settled a great number of captives in the Roman territories. (Eutr. Brev. 9.24-25).

I think the best thing to do is cross reference various primary sources with what you can scrounge up in secondary and tertiary sources, as I've started to do here, so that you can get a decent view of the political and military landscape at the time. I've focused here on a few of the battles that occurred. I hope it's been of some help.