I'm not sure I want to delve into the matter of past vs perfect at the start of this (see the bottom of this answer for this detail).
Let's consider the phrase that you have:
We can make a whole sentence for what's being said,
We can translate this into English as
The character 右 is a character that has joined 口 (mouth) with 𠂇, which expresses the right hand.
I looked in my own 小学館 kanji dictionary for the same character. Here's the explanation of the composition of the character I found there.
A character that expresses the right hand protecting the mouth
So, what I want you to notice here is there is a bit of editorial choice or style going on here in how to express the composition of the character 右. In other words, the definition you found could easily have been written as
In English, this would be
The character 右 is a character that joins 口 (mouth) with 𠂇, which expresses the right hand.
You might like "has joined" over "joins" (or visa-versa), but that's a stylistic choice. Either way, we understand what's being said. Semantically, there is perhaps a very slight difference, which I'd say is more philosophical than anything.
[Indulge me a bit in some speculation.]
When using "has joined" (あわせた) we're thinking of the character as something that was "created" sometime in the past and continues to preserve this form: so, we're thinking about the character a bit historically. When using "joins" (あわせる) we're not thinking of the character as something from the past but as something being presented to you right now in a particular form. (Really, this is rather a pedantic bit of hair-splitting speculation. Neither an English speaker or a Japanese speaker is going to necessarily analyze (or think of) it this way. I'm just presenting this interpretation as a way for you to think of these two uses: ie., to help you wrap your head around what you're encountering.)
All that said, what I also want you to notice is that it wouldn't really be quite accurate to call "a character that has joined..." something in the past. It's expressing the idea of how this was made and continues to be. The character is still the same; what's being said is not that at some point in the past it was one way and now no longer is. It continues to be the way it was constructed. This idea of something done in the past which continues to be true into the present is called the perfect. The past tense is used to express an idea that is located in the past which may (or may not) be true anymore.