any supporting evidence from medical websites or others?

Yes—but the evidence supports the general point more than it supports the exact phrase “two-tiered nipple.” Medical anatomy references recognize that nipple appearance varies, including protruding versus flat or inverted nipples, and a study of 158 adult men found measurable normal variation in nipple and areola dimensions.

• The structure is called the nipple–areola complex; the nipple is a distinct, raised central structure relative to the surrounding areola.
• There is no universal “standard” male nipple shape or a medical cutoff for how wide its base should be.
• So a stable, slightly wider or raised nipple base can reasonably be within normal anatomical variation—but an online description cannot establish that your specific finding is normal.

The reason to seek an in-person exam is a new or changing lump or thickening, a hard/irregular area, nipple inversion, skin dimpling/redness/ulceration, discharge (especially bloody), or an armpit lump.