If TIPS yields are negative, why do TIPS ETFs have a positive yield?

[T]he VTIP ETF from Vanguard has a positive yield of about 1.2% right now.

Are you sure? According to Vanguard, the 30-day SEC yield for VTIP as of 01/07/2021 is
-1.44%:

The yield quoted is the real yield, or the yield before adjusting for inflation. The actual yield of Vanguard Inflation-Protected Securities Fund will be a combination of the real yield and an inflation adjustment. A complete estimate of the fund's yield requires that an estimate of future inflation be added to the real yield. Because inflation fluctuates, it cannot be projected into the future precisely enough to be included in the yield quote. The inflation adjustment is based on changes to the Consumer Price Index (CPI) and can be either positive or negative, based on the change to the CPI. Investors interested in maintaining the purchasing power of their investment should invest their dividend distributions.

E — BASED ON HOLDINGS' YIELD TO MATURITY FOR 30 DAYS AS OF END OF PREVIOUS WEEK.

G — DOES NOT INCLUDE ANY INCOME ADJUSTMENT RESULTING FROM CHANGE IN INFLATION RATE

Assuming it has a positive yield, it's possibly due to the fact that the ETF holds a broad portfolio of TIPS purchased at different prices/points in time, whose aggregate coupons give the fund a positive yield.

For reference:

How TIPS Can Have Negative Yields

The answer is that the yield on a TIPS bond is equal to the Treasury bond yield minus the rate of expected inflation.This is an essential characteristic of TIPS–they are designed that way. As a result, when standard Treasury bonds are trading at yields that are below the expected inflation rate–as has been the case since late 2010–TIPS yields will fall into negative territory.

Let’s look at July 17, 2012, again as an example. On that day, the 10-year Treasury note was yielding 1.49%. However, based on the comparative yields of TIPS versus plain-vanilla Treasuries, investors were expecting inflation of about 2.13% in the next ten years. If you subtract this 2.13% from the 10-year yield of 1.49%, the result is a negative number for the 10-year TIPS: -0.64%. As long as Treasuries continue to offer yields below the rate of expected inflation, TIPS will remain in negative territory.

https://www.thebalance.com/why-are-tips-yields-negative-416876

EDIT #2 to address some of the comments/questions:

it seems like a strange financial instrument which hasn't even been consistent in its dividend payouts...

That's by design (emphasis mine):

Treasury Inflation-Protected Securities (TIPS)

Treasury Inflation-Protected Securities, or TIPS, provide protection against inflation. The principal of a TIPS increases with inflation and decreases with deflation, as measured by the Consumer Price Index. When a TIPS matures, you are paid the adjusted principal or original principal, whichever is greater.

TIPS pay interest twice a year, at a fixed rate. The rate is applied to the adjusted principal; so, like the principal, interest payments rise with inflation and fall with deflation.

https://www.treasurydirect.gov/indiv/products/prod_tips_glance.htm

In summary, the TTM Yield shows yield over the past year, and the 30-Day SEC Yield shows the most current yield (as of the last 30 days).

https://www.thebalance.com/difference-between-ttm-yield-and-30-day-sec-yield-2466432