Repeated measures over time It may be easier to show you visually what I am trying to compare:

This is what the table for one of the conditions might look like:

The graph above plots the mean values at each time point just so it can visualised for an audience.
Simply speaking, I am looking for a way to tell if Condition 1 produces higher counts than Condition 2 or 3 or Control etc.
I have performed a repeated measures ANOVA with multiple comparisons (Tukey correction) and wanted to check if this was an appropriate way of comparing the data. If it is, then is the best way to compare simple effects within rows or simply to compare column means.
 A: Here you have repeated measures (5 replications) of an experiment where you made measurements over 10 time points under 4 experimental conditions.
Repeated measures anova doesn't take account of the downward temporal trend here.
One alternative is to use multivariable regression, where you regress the count variable on time, with the addition of the condition variable. If time is a continous variable, that would be an ANCOVA model. To handle the repeated measures you can just include an indicator variable for the replication number. In R you would run:
model <- lm(pressure ~ time + replication + condition, data = mydata) 

One issue I see is that, initially there appeared to be a fairly obvious linear trend, which would be captured by the estimate for time variable - provided that it is coded numerically - but actually the time points are not equal, they are steps of 10 up to 60, but then steps of 30. Now that you have updated the question with a different plot, it becomes more noticeable. One way to handle this is to code the time variable as discrete, since you are not interested in the time trend itself. This would seem a sensible first step. Depending on the model fit you might them want to explore a model with time as numeric such as a piecewise linear model with 2 pieces (0-60 and 60-180) or a transformation to obtain a linear slope - such a log transform.
The estimates for condition will answer your research question. If you code the condition variable as a factor with condition 1 as the reference level then you will get 3 estimates for condition (control, condition 2 and condition 3). However, the interpretation will be different depending on how you handle time. With time as a numeric variable each of the estimates for condition will be the expected difference between condition 1 and the other levels at time=0 - so in this case you may want to centre the time variable aroud zero to make this more meaningful. If time is coded as a factor then the estimates for condition will be relative to whatever the reference level of time is. You can change the reference level to get different contrasts, though this can become unwieldy with so many time points. In order to look at the whole range of time, I believe you can use functions from the emmeans package, but this is not something I usually do so I can't comment much further than that.
Another alternative is to use a mixed effects model, with random intercepts for replication. Arguably, 5 replications is too few to fit random itercepts but I would still consider it. The random intercepts take care of the repeated measure. The base model formula would look something like this:
model <- lmer(pressure ~ time + condition + (1|replication), data =  mydata)

The considerations about the time and condition variables above would equally apply here.
lmer is a function from the lme4 package in R.
