Yes, you're right. It doesn't matter how much your employees' salary is; you need to register if:
Eligibility Under Section 2(12) of the Act
Under Section 2(12) of the Act, it is applicable to non-seasonal factories employing 10 or more persons.
Eligibility Under Section 1(5) of the Act
Under Section 1(5) of the Act, the Scheme has been extended to shops, hotels, restaurants, cinemas, including preview theatres, road-motor transport undertakings, and newspaper establishments employing 20 or more persons.
Furthermore, under Section 1(5) of the Act, the Scheme has been extended to Private Medical and Educational institutions employing 20 or more persons in certain States/UTs.
Please read further for all frequently asked questions about ESI:
https://biblehr.com/esic-frequently-asked-questions/
On a side note, the ESI new wage limit of Rs 21,000/- is under consultation. You need to wait until the final approval.