Hmm I think I know what's happening. Since every point on the plot is getting its own geom_tile(), the colors are darker in cases where there is more than one point in the same row (because successive tiles of the same color are being overlaid one on top of the other). I didn't realize that would happen because my little toy dataset did not have datapoints that fell in the same Y-axis "row".

So I have a workaround for you. I'll use my original toy example, modified with an additional point in the Photosynthesis row to illustrate how this works. Basically what we'll do is create a new column called typefill that will be used to set the fill for geom_tile(). Since each "row" can have overlapping geom_tile()s we are going to set the value in typefill conditionally. The condition is this: we will group all the rows (of the data.frame()) together that have the same GO_term (Y-axis value) and Type (our original geom_tile() fill value). Now for each of these groups of rows, we assign the Type value of the group as the typefill value of the first row of that group; all other rows just get an NA. The result is that when we plot the data now, and pass typefill to geom_tile()'s fill parameter, we will no longer have overlaid colors as we saw in your output as the fill is being set only once.

library(ggplot2)
library(dplyr)
library(magrittr)
library(tidyr)
library(ggplot2) #for plotting
library(forcats) #for plotting

#Toy data.frame
mydat <- structure(list(GO_term = structure(c(2L, 4L, 3L, 1L, 4L), 
                                            .Label = c("Kinase", "Metabolism", "Nucleus", "Photosynthesis"), 
                                            class = "factor"), 
                        Number = c(5, 10, 15, 16, 20), 
                        Class = structure(c(3L, 2L, 1L, 1L, 2L),
                                          .Label = c("hs", "hzs", "start_duf"), class = "factor"), 
                        Type = structure(c(1L, 1L, 2L, 3L, 1L), 
                                         .Label = c("BP", "CC", "MF"), 
                                         class = "factor")), 
                   class = "data.frame", row.names = c(NA, 5L))




#First we group by Type and GO_term, and assign a "yes" to the first row
#and "no" to every other row of the grouping
mydat %<>% 
  group_by(Type, GO_term) %>%
  mutate(typefill = if_else(row_number() == 1, "yes", "no")) %>%
  ungroup()
#Then in the whole data.frame, typefill = "yes" will be replaced by the Type value
#from that row, and typefill = "no" will be replaced with NA
mydat %<>% mutate(typefill = ifelse(typefill == "yes", as.character(Type), NA))


#Plotting, now pass typefill to geom_tile's fill parameter instead of Type
ggplot(mydat, aes(y = reorder(GO_term, as.numeric(Type)), x = Number, size = Number)) + geom_point(aes(color = Class), alpha = 1.0) + 
  geom_tile(aes(width = Inf, fill = typefill), alpha = 0.4) + 
  scale_fill_manual(values = c("green", "red", "blue"))

And this is the result:

Of course, you now have that one extra NA column in the legend, but that can be hidden quite easily.