Analysis of information sources in references of the Wikipedia article "Άβαροι" in Greek language version.
It must be the case then that the anonymous author of Constantine’s major source on the Croats was the same one who wrote that the Avars lived in Dalmatia, since he overstretched Dalmatia as far as up to Danube to be able to include the territory of Lower Pannonia recorded in the DCBC. It was then this same anonymous author who made this confusion about the Avars living in Dalmatia, not Constantine.
An Avar embassy first appeared in Constantinople in 558, asking for land within the empire and calling for an annual subsidy. Justinian granted them a subsidy, but for land he directed them elsewhere.
[...] the first thing the Avars did when they came near the Caucasus on their flight from Central Asia was to send an embassy to the aging emperor Justinian. That took place sometime in winter 558/59, and they struck the usual deal: the Avars were to fight for the Empire against unruly gentes and in turn would receive annual payments and other benefits. Indeed, for 20 years to come the Avars, under their Khagan Baian, fought Utigurs and Antes, Gepids and Slavs, whereas their policy towards the Empire relied more on negotiation than on war.