The 37 year-old says the main reason for him making the switch to Mount Wise is the promise of help towards the cost of professional physiotherapy treatment as he continues his recovery from a double ankle break sustained during Town's Charity Bowl match against Bodmin in August.
"I've got to be honest, that's my biggest motivation for leaving," Drummond told the Packet.
"Unfortunately Falmouth haven't had a physio this year, and since I broke my ankle I've been paying for my own, which has cost a lot over time. I've asked Falmouth if I could get a professional physio but they've always said no. They used to have one, but he finished and they've not replaced him.
"Newquay have asked me to go across and they've said they'll give me all the help they can, and I can only thank them for that. The physio there spotted I wasn't right straight away.
"It's attractive because it's a very professional outfit and they're still in two cups. I don't know how long I'm going to be able to carry on, and I've got to look after number one."
Falmouth Town co-manager Les Gilbert expressed his disappointment at Drummond's decision to leave the club, but said he was not made of aware of the player's concerns.
"He phoned me on Saturday morning and mentioned this thing about us not having a physio," said Gilbert. "It's the first I've heard of it. He's not mentioned anything about that to me before - not a word - so I don't know why it's suddenly become such a major issue.
"If it had been brought to our attention I'd have done something about it, but I'm not stupid. I want people who want to be at this club. I'm not going to waste my time on people who want to leave."
Co-manager Robbie Stephens echoed Gilbert's sentiments, saying: "It's a feeble excuse in my book.
"He sat down with us in the clubhouse a month ago and never mentioned it. He said he was training and he never mentioned that to us at all."
The move is likely to further strain Falmouth's relationship with Newquay - a club Gilbert and Stephens have managed - following the transfers of Mark Vercesi, Wayne Quinn and Jamie Devine.
Quinn and Devine's transfers have proven particularly controversial after they were accused of taking advantage of a loophole in Peninsula League rules which prevent the signing of more than one player from the same club in a 28-day period.
The pair signed for St Dennis and Exmouth respectively before making the switch to Mount Wise at later date.
In contrast, Drummond's transfer was the result of direct contact between the two clubs. But the striker admits that recent transfer activity may have tarnished the Peppermints' reputation.
"Unfortunately it goes on all the time," he said.
"The manner in which they've done it people aren't very happy with and I suppose the fact they've done it on several occasions hasn't helped their case across the county.
"But all managers try and get around the seven day rule [the period of notice a club must give before approaching a player], anyone in football would know that."
Drummond also expressed his sympathy for Falmouth's current predicament.
"I said to Les I feel really sorry for those two," he said. "They're going to really struggle because there's no budget there and they've been out of the game for a while.
"I think things have changed a lot since they were last involved. Fortunately they've got enough points to keep them up this season."
Gilbert responded by saying: "I don't think the game's changed that much has it? The ball's still the same shape. It's all a little bit silly to be honest. What's irritating to me is these people are saying that Falmouth are going down the pan and it's absolutely not true.
"We've got funds available at the club. It's a sensible budget that myself and Rob are comfortable with. We're in a transitional period and we're not going to throw money at our problems like some other clubs do."
Stephens agreed, saying: "People have changed perhaps, but the game's the same.
"And those people say Falmouth town are going down the pan, but that's rubbish. Falmouth Town will never go down the pan, and certainly not while me and Les have anything to do with it."