VHA-TPG merger: TPG wanted to keep Singapore division, but Vodafone don't want. As the company is 50.1% Vodafone AU, 49.9% TPG (which is further divided into different shareholders), TPG have no choice but to spin off the Singapore division.
TPG (TPG Telecom Limited) already had Tuas (Tuas Pty Ltd), which owns TPG Singapore (TPG Telecom Pte Ltd) and Tuas Solutions Sdn Bhd. So with the split, Tuas will become a full separate entity on it's own, with a new ticker in ASX (TUA).
TPG Telecom Limited will be rebranded as TPG Corporation. Vodafone Hutchison Australia Pty Limited and TPG Corporation will merge, and is called TPG Telecom Limited. Ticker will change from TPM to TPG in ASX. Not sure what will happen to HTA though.
So no, Tuas did not buy TPG Telecom Pte Ltd. They're just a spin off from existing TPG Telecom Ltd.
All existing ASX: TPM shareholders will get a special dividend that includes additional shares for ASX: TUA when it starts operating, while their existing shares will be converted to ASX: TPG.
Tuas Limited will still get up to 3 years of financial aid from TPG Limited as part of compensation from the demerger, to aid in completing rollout of nationwide network. TPG Branding will also be royalty free for up to 2 years from date of demerger, but they must rebrand by the time it ends.