First of all, congrats! Great achievement to receive an offer, especially in the competitive SG market.
On the revision of role offered - sorry to hear that they changed the offered role last minute. I've seen this happen at times, as the fit for a role crystallizes throughout the recruiting process - yet, must be frustrating. Given you have no prior consulting experience, however, they may actually be doing you a favor in disguise.
Many people underestimate how challenging a direct start on Manager level can be. As a matter of fact, at MBB firms as one example, non-experienced laterals hired straight into Manager level show the highest churn rates (forced and unforced). I'd expect it to be similar with Deloitte - hence, would be careful.
Consulting firms have high expectations and limited patience, so it would be advisable for most people to spend a bit of time honing core consulting skills, before assuming EM responsibility, where you will be fully exposed from the start.
Hence, if you consider and manage to negotiate a senior consultant role with tenure (i.e. means faster promotion) you could still turn this into a positive, not to say better outcome, that prepares you better for longer-term career success. Alternative, of course would always be to insist on Manager level and try to hard ball (only advisable, if you have solid enough alternatives at hand).
On the salary range question - I do have actual comp data points for both Senior Consultant and Manager levels at Deloitte SG. Same is true for MBB and some Tier 2s as benchmark. Feel free to reach out via PM, if you'd like to learn more / discuss.
Hope this helps.