That's an interesting site about Tempelhof's history.
BEA was all Viscount at Berlin by 1960. Their competition was Pan Am with DC-6Bs, and the Viscounts were preceived better. When Pan Am introduced the 727s in 1965 BEA was suddenly at a disadvantage, and they refitted some Viscounts with better seat pitch etc and they operated as a subfleet within BEA out of Berlin.
The Viscount's replacements were the fleet of One-Elevens that came in 1968-69. This coincided with Air France giving up their small IGS operation (which always operated out of Tegel, and they had used Caravelles latterly) and going into a cooperation with BEA. For this reason the BEA branding was taken off the new One-Eleven fleet, they operated with plain blue tails with just "Super One Eleven" written on them, and with joint BE/AF flight numbers.
In the 1960s there was also a Pan Am daily 707 service to New York via Hamburg, but the 707 could not operate out of Tempelhof so this always used Tegel.
The German holiday companies used German charter flights to the Mediterranean from other German airports, but from Berlin they had to use Allied airlines. Dan-Air was to the fore here, I presume they had a crew base there. Other UK charter companies came and went over time, although runway restrictions meant they really favoured Tegel.
Due to the 4-powers restrictions operators from Berlin had to use pilots who were nationals of their own countries, but the cabin crew were locally-recruited Germans.