You can only apply under one financial requirement category (unless the UK job offer doesn’t meet the minimum income requirement and then you can use savings to top it up), so you likely would be using either:
- Guaranteed UK job offer paying at least £18,600, plus last 12 months of income in the US showing at least £18,600 made by the UK citizen in the US (Category B)
OR
- Last 1 or 2 years of self-employment income (average of £18,600 per year) plus evidence that that self-employment income is guaranteed to continue at a level of £18,600 or more per year in the UK (Category F or G – tricky category as it’s difficult to meet all the requirements and provide all the required documentation for self-employment income and it’s hard to prove that you will have guaranteed self-employment work in the UK right away after you move)
OR
- £62,500 in savings, which have been held in your account for a minimum of 6 months (Category D)
If when you apply, your savings have not been in the account for at least 6 months, they will not be considered for the visa and will not count for anything, so you wouldn’t be able to use any of your savings to meet the requirement (i.e. there’s no point including any evidence of them).
If they have been in the account in full for 6 months, then you can use savings as your sole evidence if you have £62,500 or more, or they can be used as evidence to top up the other categories if you cannot meet the £18,600 UK salary for Category B or F/G. However, the first £16,000 of savings do not count and then you need on top of that first £16,000, 2.5 times the difference between his UK salary and £18,600.
For example, if he has earned £18,600 in the US in the last 12 months, but his UK job offer pays only £15,000, then you won’t be able to qualify for the visa unless you also have at least £25,000 in savings (£16,000 + (2.5 x £3,600)).
But if you can meet Category B or Category F/G on their own, then you do not need to show any evidence of savings anyway.
You can read more about each financial requirement category and what evidence you need to meet each one here:
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/371437/AnnexFM_Section_FM_1_7_Financial_Requirement.pdf