This is actually more of a historiography question really, so I hope you’ll bear with me here…

Did Isaac sometimes communicate with Saladin? Yes! Did the German crusaders believe Isaac and Saladin had made a secret alliance to stop the crusade? Also yes! But is that what actually happened? Maybe not!

The crusaders may not have really understood what (if anything) Isaac did, they had other motives for criticizing the Byzantines, and all three sides may have misinterpreted the events and each others’ motives. Modern historians differ on whether there was an alliance at all, and everything depends on how we interpret the medieval accounts.

First, a bunch of complicated things happened in the Byzantine Empire in the 1170s and 1180s. In 1176 the Seljuk Turks won the Battle of Myriokephalon against Emperor Manuel I, and took control of most of Anatolia. Manuel died in 1180 and was succeeded by his son Alexios II, who was still a child. Alexios’ mother, Maria of Antioch, was regent for her son, but there were anti-Latin riots (Maria was from the ruling family of crusader Antioch, so technically she was a Latin westerner) and Alexios and Maria were overthrown and murdered by Andronikos Komnenos (Maunel’s cousin) in 1182. Andronikos was a notorious troublemaker who had mostly spent his life having strange adventures, like running off with his cousin Theodora (who was married to the crusader king of Jerusalem at the time), and now he was the emperor in Constantinople.

There was a massive anti-Latin riot as soon as Andronikos came to power and tens of thousands of Genoese and Venetian merchants were killed (the “Massacre of the Latins”; the numbers may be exaggerated but there was certainly a widespread massacre). He also faced invasions from Hungary and Sicily in 1185, and he turned out to be so unpopular that he too was overthrown and murdered, by Isaac Angelos, who became Isaac II.

At the same time, the Byzantine province of Cyprus rebelled against Andronikos as well, and a breakaway Komnenos dynasty was established there. Meanwhile, down in the crusader states, almost the entire Kingdom of Jerusalem was conquered by Saladin in 1187 - except for Tyre, which was relieved by Conrad of Montferrat. Conrad was related to the ruling dynasty of Jerusalem, and he was also a cousin of the Holy Roman Emperor Frederick. The loss of Jerusalem led to the Third Crusade and Frederick’s eventual arrival outside Constantinople in 1190.

All that is very important for the background for the supposed alliance...but here is where we get into historiography and modern interpretations.

The main source for the alliance is the chronicle of Magnus, a monk in the Austrian abbey of Reichersberg. Magnus wasn’t on the crusade, but he copied a letter that was supposedly sent from the crusader states in 1188, maybe by Conrad in Tyre. According to this letter, when the Normans and Hungarians invaded the Byzantine Empire, Andronikos tried to make an alliance with Saladin. Andronikos:

"insistently urged him that he might do homage to him, since he was emperor, and in return he would be ready to bring help to him when urgently needed, if he had the resources and Saladin requested this. Furthermore they joined together and then swore to this agreement, that if Saladin succeeded in occupying the land of the men of Jerusalem with his advice and assistance, then Saladin would keep some land for himself, but would leave Jerusalem and all the coastal area apart from Ascalon free, on condition however that he would hold it from the aforesaid emperor, and that they might acquire Iconium and the land of the sultan [i.e. the Seljuk sultan of Rum in Anatolia], and the land as far as Antioch and the territory of the Armenians would belong to the aforesaid emperor, if they could gain it..." (Chronicle of Magnus of Reichersberg, pg. 153-154)

Andronikos was killed before Saladin responded, but the letter also says that while Andronikos was in power, Isaac Angelos fled to Muslim territory and was also in contact with Saladin. Isaac confirmed the exact same treaty with Saladin when he became emperor, “since he both hated and feared the Latins”. This was why Saladin attacked the crusader states in 1187, with help from a Byzantine fleet. They then began sending each other increasingly lavish gifts - Saladin sent him various things including an elephant, and Isaac sent him a golden crown and three hundred beaver pelts, then Saladin sent back

"a baby elephant and a little beast that makes musk, an ostrich and five leopards...and a vessel of solid silver that could hold twenty measures of wine, full of most strong poison" (Chronicle of Magnus of Reichersberg, pg. 155)

When they demonstrated the poison to the Byzantine ambassadors, the fumes alone instantly killed a crusader prisoner. Saladin also promised to restore the churches in the Holy Land to the Greek church (replacing the Roman rite that the crusaders used), and Isaac would allow a mosque to be established in Constantinople.

Now, the question is, should this letter be taken seriously or not? Clearly some of it is a bit outlandish, but is the general idea accurate? Charles Brand, who is perhaps a bit old and out of date these days, considered it to be genuine, and that:

"From 1185 to 1192 the alliance with Saladin was the cornerstone of Byzantine politics" (The Byzantines and Saladin, pg. 178)

Brand argued that Isaac was afraid the Germans would take revenge for the Massacre of the Latins, and that the alliance with Saladin was the reason that he imprisoned the German ambassadors while Saladin’s ambassadors were also in Constantinople, that he refused to meet with Frederick, etc.

Brand admits, however, that the only Byzantine source for this period, Niketas Choniates, makes no mention of any alliance. But he suggests this may have been out of embarrassment, or because, as you said, it was supposed to be “secret” (although it doesn't seem to have been very secret at all, according to Magnus’ chronicle).

Magnus is the only source that gives this much detail, but the idea that there may have been an alliance of some sort can also be found in other medieval European chronicles. Conrad, as well as Sibylla, the Queen of Jerusalem, sent other similar letters to the west that were copied into various English and French chronicles.

Correspondence between Isaac and Saladin is also preserved in Arabic chronicles. Once the Germans passed through Constantinople, Isaac tried to convince Saladin that the crusade was not a threat:

"They have been so weakened that they will hardly reach your lands. If they do arrive, they will be weak, having suffered much and will be no benefit to their kindred and no harm to your Excellency." (The Rare and Excellent History of Saladin, pg. 123)

So clearly there was contact, if not an actual alliance. Of course, Isaac was totally lying - he hadn’t really weakened the Germans, and if Frederick hadn’t accidentally drowned in a river along the way, they might have been a good match for Saladin. Saladin didn’t appreciate Isaac’s blatant dishonesty and eventually stopped responding to Isaac’s letters.