That's not a universal rule, no! And certainly not for people who aren't used to reading manga. Since you have two people speaking in the preceding panels, it's impossible for the reader to know which character is continuing to speak unless clearly indicated.
In the third panel, for example, the bubble on the left has a small tail (might wanna make it bigger and more visible!) points towards the greyhaired character - but the bubble on the right side of the panel doesn't have a tail! So I don't know if the greyhaired character is continuing to speak, or if the blonde one is taking over. Adding a tail to that bubble would help! Also, you can connect bubbles with arced tails. Here's how I do it:
See the bubbles in the middle of the page? They're connected with an arced tail, which means they're spoken by the same person, but don't cover up as much of the background space as merging the two bubbles together would.
Another thing to keep in mind when planning speechbubbles is the reading flow. It should be easy to follow from one to another, and they should lead the readers' eyes across the page from panel to panel in the right order. The way you have arranged your bubbles here is also part of what is confusing your readers (and me).
Example-time!
Fig 1: The order we are (I assume) intended to read the bubbles:
You can see it's a pretty complicated, wiggly arrow I've had to draw here. Your readers' eyes have to zig-zag quite a bit to get to the final bubble in this section!
Fig 2: The way the eyes actually move across the page:
You can see that the most natural, left-to-right way of reading has the eyes move from bubble 2 to bubble 4 before hitting bubble 3 on the way back. When moving back to the left to start a new row, we hit the top of bubbles 9 and 7 in reverse order before we hit 5, dip down to 6, and head back right across 8 and 10.
This is because those of us who read written language from left to right are so used to prioritizing left-to-right as being more important than vertical directions that if we aren't focusing tightly, this is the most natural flow of our eyes across the page.
Fig 3: The intended split between rows of panels:
The orange line is where the top row of panels is divided from the bottom row of panels by the gutter (i.e: space between panels). You've filled the gap with colour and speed-lines instead of white, but that's still where the gap between the two rows is intended to be, and how we're intended to read them.
You can see the orange line I've drawn actually passes straight across several of your bubbles, either through the text or clipping the top edges of them.
Fig 4: The panel-row split incorporating the bubbles:
Drawing a panel-row split line that actually includes the bubbles themselves results in, again, a pretty squiggly line, as you can see. You've overlapped the speechbubbles happening in one panel with panels happening later in the sequence. What this does is lead the reader's eye across two panels that aren't in sequence. If I were to read bubbles 2 and 3 in order, it would mean that my eye would move from panel 2 to panel 5 - since bubble 3 overlaps with panel 5 - without hitting panels 3 and 4 in between. I would then have to go back up to panel 2 to finish reading bubble 4, before moving to the left to hit panel 3.
You can see how it gets confusing in a hurry.
