This statement is widely regarded as true.
This article bases some of its claims off of actions on Wall Street, using raising bond rates as evidence that many people believe inflation and interest rates will raise. It's hard to dispute the claim made, because it states that his plan "COULD" lead to higher interest rates. This is ultimately true, because it's impossible to predict the future and in that sense, anything "could" increase interest rates.
As far as tariffs raising consumer prices, this will likely happen. Trump's plan is to increase tariffs in an effort to bring manufacturing jobs back into the national economy, and minimize the amount of reliance on other nations. This will result in an immediate increase in consumer prices though, because international producers will have to pay more to ship their product, meaning they will raise the price to counter the increase in taxes.