Tye was hastily flown out of India on Sunday night after requesting a release from the Rajasthan Royals on personal grounds.
On Monday, Royal Challengers Bangalore announced that leg-spinner Zampa and paceman Richardson had been given permission to return home for personal reasons.
Meanwhile, Australia's Test vice-captain Pat Cummins is staying put - for now - and has donated $50,000 to go towards more oxygen supplies for India's under-pressure hospitals.
The star fast bowler encouraged other IPL cricketers to help out in India's desperate fight against coronavirus.
"At times like this it is easy to feel helpless. I've certainly felt that of late," Cummins wrote on social media.
"But I hope by making this public appeal we can all channel our emotions into action that will bring light into people's lives.
"I know my donation isn't much in the grand scheme of things, but I hope it will make a difference to someone."
West Australian Tye was able to fly to Doha, before getting a connecting flight to Australia to start two weeks in quarantine.
It's understood his decision had more to do with bubble fatigue, after having lived in hubs virtually uninterrupted since Australia's trip to England last August.
However, the IPL withdrawals come amid growing unease, with the Australian government - having already reduced passenger numbers from India - reportedly set to discuss a temporary ban on all repatriation flights from the country on Tuesday.
More than a million people have been diagnosed with the virus in India in the past three days, while Australia has restricted incoming passenger numbers.
The IPL is continuing in a COVID-safe bubble, but Australian Daniel Sams caught the virus on arrival in India.
Cummins noted there was quite a bit of discussion about whether it was appropriate to continue playing the IPL as the crisis deepens. He said he had been told the Indian Government believed the IPL provided a few hours of respite for the country at a difficult time.
Both Cricket Australia and the Australian Cricketers' Association are adopting a watch-and-wait approach, with both organisations in constant contact with players.
As it stands, players organise their own flights out of India given the tournament is during their holiday period.
On signing a no objection certificate (NOC) with CA to play in the tournament, players were told there would not be chartered flights home.
However, the situation has since worsened in India and CA will not leave players stranded if there is no other way to return them home.
Ricky Ponting, who is in India as coach of the Delhi Capitals, described the situation as "grim".