Actually, there are some differences between Reference Check and Background Check.

Background Check covers highest academic, minimum 8 years employment history, criminal, CCRIS/CTOS, bankruptcy, sex offend, Industry Court Cases, sanction list and many other formal critiria (depending on the requirement from the employers). Established MNC, especially those American companies, have implemented this process locally for many years. On 18 Mar 2018, BNM has issued a policy (https://www.bnm.gov.my/-/employee-screening-09032018) that all employers in the finance/banking/insurance industries must conduct background checks effective from 1 July 2018. Service providers for the Background Check need formal authorizations from the candidates before conducting the checks. Candidates have the right to request for delaying (or excluding) the checking on the current employment until joining the new employer.

2. Reference Check usually are conducted by HR/Recruitment Agency. The checks are mainly for subjective info e.g. contacting previous supervisors, colleagues, co-workers to verify the attitudes, team-work, and etc. Nowadays, upon the request from the clients, most of the recruitment firms will do these before the issuance of the formal offer. Typically, most of recruitement firms will also do this for own benefit in order not to waste too much efforts in candidates who are likely to be rejected.

My advice to you:

1. Drop the myth of 3x exchange rate. You should look into the JD and the market rate in Singapore. Living standard in Singapore is higher than Malaysia.
2. You can find the estimated market rate from the annual salary survery conducted by recruiters such as

https://www.robertwalters.com.sg/salarysurvey.html
https://www.michaelpage.com.sg/salary-guide
https://www.glassdoor.com/Salaries/singapor...123_KO10,18.htm