hi Dew,
Your right, the birthstone of a person goes by the month they were born. You dont need anything else to know this.
January
Genuine Stones: Garnet
February
Genuine Stones: Amethyst
March
Genuine Stones: Aquamarine / Blue Topaz
April
Genuine Stones: Diamond / White Topaz / White Zircon
May
Genuine Stones: Emerald
June
Genuine Stones: Alexandrite / Pearl / Rhodalite
July
Genuine Stones: Ruby
September
Genuine Stones: Sapphire
October
Genuine Stones: Opal
November
Genuine Stones: Citrine / Yellow Topaz
December
Genuine Stones: Blue Zircon / Blue Topaz
Blessings
RA