Pronunciation of the word Pǔtōnghuà

I am pronouncing the word Pǔtōnghuà 普通话/普通話 as [pʰ᷆u˨˩·tʰʊ́ŋ˧˥·xû̯ä˥˩] with the first syllable being pronounced with a 低降调 low falling tone (調值 21). However, I was told that I should pronounce the first syllable with a 低降升调 low falling-rising tone (調值 214) like this [pʰ᷉u˨˩˦·tʰʊ́ŋ˧˥·xû̯ä˥˩].

I do believe I am using the correct tone, but I am learning Mandarin, whereas the person telling me I am wrong is a native Chinese speaker.

I do understand the pīnyīn spelling includes a caron on the first syllable and the caron represents the 3rd tone in Mandarin Chinese. However, since the first syllable is followed by a syllable with a 阴平声 high tone (調值 55), then wouldn't the first syllable be pronounced with a 低降调 low falling tone (調值 21)?