Short answer, the citations of probabilities, and the language used to describe them, should reflect what was done. For example, for ANOVA, the regression probability reflects how likely that regression fit is to occur by chance alone, thus although one-tailed, one would not usually refer to that fact.
When the probability of a test statistic occurring by chance alone is from a difference, that likelihood includes the areas of the density function of that statistic both more extremely lesser than and greater than the observed value. For a one-tailed test, one is concerned with areas only either more extremely greater than or lesser than the observed value, but not both and is thus 1/2 of the null hypothesis probability of both extremes for symmetric distributions like the W-statistic of the nonparametric Wilcoxon signed-rank test. For those distributions that are asymmetric and two-tailed, e.g., this, the doubling rule would not hold.
For intraclass correlation there is a rating scale but no hypothesis testing per se.
For Spearman's rank correlation significance testing, the test is essentially one-tailed, and ditto for ANOVA F-statistic testing two-way repeated measures. However, the confidence intervals for parameter values are two-tailed, so it depends what one is talking about within the ANOVA procedure. Friedman's test is nonparametric one-way ANOVA, so its interpretation is similar to other ANOVA.