That is not correct. The portion of your capital gains that are not excludable are added to your other taxable income to determine the capital gains tax rate. If the total taxable income including the capital gains is below the limit for 0% capital gains tax, the capital gains would be taxed at 0%. If some of the gains exceed the 0% capital gains limit, the excess would be taxed at 15% and then 20% for any gains in excess of the 15% limit.
Here are the capital gains tax rate ranges:
Tax rate Single Married Filing Jointly Head of household
0% $0 to $38,600 $0-$77,200 $0-$51,700
15% $38,601-$425,800 $77,201-$479,000 $51,701-$452,400
20% $425,801 and up $479,001 and up $452,401 and up
