Is the IRS supposed to correct my earned income amount on my tax return transcript if it's not showing the accurate amount? ?

Once filed, the original return stays the same.  If you amended your return, only the Account transcript is updated.

If you make a math error when preparing your return, (2 = 2 = 5) IRS will make a math error correction and send you a notice telling you what it did. IRS will not have your reported income information until after the filing season is over. If you under-report your income and tax due in about a year you will get a notice proposing additional tax. If you reported too much tax IRS will assume you are reporting income it wasn't told about.

If they find an error, they may fix it and assess new tax based on the correct number, unless you fix it yourself first (recommended).

What is an account tax transcript? The tax return transcript is what you filed in IRS 1040 in a certain year, or an updated one based on their audit or your update. If the IRS tax transcript for a filed year shows a higher number than your records, you should have been sent a notice by the IRS in the mail about a tax audit and raise of your income. If a lower number, you misfiled, and you re-file with a 1040X for that year.

Per comment - IRS is the United States, unless otherwise stated. Bank records do not have your income unless you work for the bank. I don't believe you understand income tax filing in the USA.